{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T07:44:48Z","timestamp":1762069488778,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T00:00:00Z","timestamp":1664150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101168","LQ22A010014"],"award-info":[{"award-number":["12101168","LQ22A010014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101168","LQ22A010014"],"award-info":[{"award-number":["12101168","LQ22A010014"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present note, we characterize Clairaut semi-invariant Riemannian maps from cosymplectic manifolds to Riemannian manifolds. Moreover, we provide a nontrivial example of such a Riemannian map.<\/jats:p>","DOI":"10.3390\/axioms11100503","type":"journal-article","created":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T03:34:17Z","timestamp":1664163257000},"page":"503","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A Study of Clairaut Semi-Invariant Riemannian Maps from Cosymplectic Manifolds"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7502-0239","authenticated-orcid":false,"given":"Rajendra","family":"Prasad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Astronomy, University of Lucknow (U.P.), Lucknow 226007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1175-6423","authenticated-orcid":false,"given":"Abdul","family":"Haseeb","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2118-4374","authenticated-orcid":false,"given":"Sushil","family":"Kumar","sequence":"additional","affiliation":[{"name":"Shri Jai Narain Post Graduate College, University of Lucknow (U.P.), Lucknow 226001, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1214-5701","authenticated-orcid":false,"given":"Sumeet","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dr. Shree Krishna Sinha Women\u2019s College Motihari, Babasaheb Bhimrao Ambedkar University, Bihar 845401, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1090\/conm\/132\/1188447","article-title":"Riemannian maps between Riemannian manifolds","volume":"132","author":"Fischer","year":"1992","journal-title":"Contemp. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1142\/S0219887810004324","article-title":"Invariant and anti-invariant Riemannian maps to Kahler manifolds","volume":"7","year":"2010","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.indag.2011.10.003","article-title":"Semi-invariant Riemannian maps from almost Hermitian manifolds","volume":"23","year":"2012","journal-title":"Indag. Math."},{"key":"ref_4","first-page":"1143","article-title":"Slant Riemannian maps from Kenmotsu manifolds into Riemannian manifolds","volume":"13","author":"Prasad","year":"2017","journal-title":"Glob. J. Pure Appl. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3999","DOI":"10.2298\/FIL1713999P","article-title":"Slant Riemannian maps from an almost contact manifold","volume":"31","author":"Prasad","year":"2017","journal-title":"Filomat"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"449","DOI":"10.2989\/16073606.2013.779968","article-title":"Slant Riemannian maps from almost Hermitian manifolds","volume":"36","year":"2013","journal-title":"Quaest. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"62","DOI":"10.56947\/gjom.v9i1.451","article-title":"Semi-slant Riemannian maps from Cosymplectic manifolds into Riemannian manifolds","volume":"9","author":"Kumar","year":"2020","journal-title":"Gulf J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1007\/s10587-014-0152-3","article-title":"Semi-slant Riemannian maps into almost Hermitian manifolds","volume":"64","author":"Park","year":"2014","journal-title":"Czechoslov. Math. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"19","DOI":"10.32513\/tbilisi\/1546570882","article-title":"Semi-slant Riemannian maps from almost contact metric manifolds into Riemannian manifolds","volume":"11","author":"Prasad","year":"2018","journal-title":"Tbilisi Math. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1007\/s00009-016-0817-2","article-title":"Hemi-slant Riemannian Maps","volume":"14","year":"2017","journal-title":"Mediterr. J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"477","DOI":"10.35378\/gujs.746652","article-title":"On quasi-hemi-slant Riemannian maps","volume":"34","author":"Prasad","year":"2021","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_12","unstructured":"Bishop, R.L. (1972). Clairaut submersions. Differential Geometry (In Honor of Kentaro Yano), Kinokuniya."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.11650\/tjm.19.2015.5283","article-title":"Einstein conditions for the base of anti-invariant Riemannian submersions and Clairaut submersions","volume":"19","author":"Lee","year":"2015","journal-title":"Taiwan. J. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3885","DOI":"10.2298\/FIL1712885T","article-title":"Lagrangian submersions from normal almost contact manifolds","volume":"31","year":"2017","journal-title":"Filomat"},{"key":"ref_15","first-page":"707","article-title":"Clairaut anti-invariant submersions from cosymplectic manifolds","volume":"41","author":"Aydin","year":"2019","journal-title":"Honam Math. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF00181419","article-title":"Lorentzian Clairaut submersions","volume":"63","author":"Allison","year":"1996","journal-title":"Geom. Dedicata"},{"key":"ref_17","first-page":"139","article-title":"A generalization of Clairaut\u2019s theorem and umbilic foliations","volume":"2","author":"Aso","year":"1991","journal-title":"Nihonkai Math. J."},{"key":"ref_18","first-page":"365","article-title":"On a decomposition of Riemannian manifolds","volume":"7","author":"Gauchman","year":"1981","journal-title":"Houst. J. Math."},{"key":"ref_19","first-page":"231","article-title":"A note on *-conformal and gradient *-conformal \u03b7-Ricci solitons in \u03b1-cosymplectic manifolds","volume":"44","author":"Haseeb","year":"2022","journal-title":"Honam Math. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.55730\/1300-0098.3151","article-title":"Clairaut semi-invariant Riemannian maps from almost Hermitian manifolds","volume":"46","author":"Kumar","year":"2022","journal-title":"Turk. J. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12077","DOI":"10.3934\/math.2022671","article-title":"Yamabe constant evolution and monotonicity along the conformal Ricci flow","volume":"7","author":"Li","year":"2022","journal-title":"AIMS Math."},{"key":"ref_22","first-page":"6195939","article-title":"Some eigenvalues estimate for the \u03d5-Laplace operator on slant submanifolds of Sasakian space forms","volume":"2021","author":"Li","year":"2021","journal-title":"J. Funct. Space"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8554738","DOI":"10.1155\/2021\/8554738","article-title":"Homology groups in warped product submanifolds in hyperbolic spaces","volume":"2021","author":"Li","year":"2021","journal-title":"J. Math."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Li, Y., Alkhaldi, A.H., Ali, A., and Laurian-Ioan, P. (2021). On the topology of warped product pointwise semi-slant submanifolds with positive curvature. Mathematics, 9.","DOI":"10.3390\/math9243156"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, Y., Khatri, M., Singh, J.P., and Chaubey, S.K. (2022). Improved Chen\u2019s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms. Axioms, 11.","DOI":"10.3390\/axioms11070324"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"9309","DOI":"10.3934\/math.2021541","article-title":"Biharmonic submanifolds of K\u00e4hler product manifolds","volume":"6","author":"Li","year":"2021","journal-title":"AIMS Math."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, Y., Mofarreh, F., Dey, S., Roy, S., and Ali, A. (2022). General Relativistic Space-Time with \u03b71-Einstein Metrics. Mathematics, 10.","DOI":"10.3390\/math10142530"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s00006-020-01097-1","article-title":"Geometric Algebra of Singular Ruled Surfaces","volume":"31","author":"Li","year":"2021","journal-title":"Adv. Appl. Clifford Algebr."},{"key":"ref_29","first-page":"795","article-title":"Quasi hemi-slant submanifolds of Kaehler manifolds","volume":"42","author":"Prasad","year":"2020","journal-title":"Honam Math. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"253","DOI":"10.4134\/BKMS.b160082","article-title":"Circles along a Riemannian map and Clairaut Riemannian maps","volume":"54","year":"2017","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s00009-017-1028-1","article-title":"Clairaut anti-invariant submersions from Sasakian and Kenmotsu manifolds","volume":"14","author":"Aydin","year":"2017","journal-title":"Mediterr. J. Math."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s00009-022-02018-1","article-title":"Clairaut anti-invariant Riemannian maps from Kahler Manifolds","volume":"19","author":"Yadav","year":"2022","journal-title":"Mediterr. J. Math."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"\u015eahin, B. (2017). Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier\/Academic Press.","DOI":"10.1016\/B978-0-12-804391-2.50003-8"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Blair, D.E. (1976). Contact Manifolds in Riemannian Geometry, Springer. Lecture Notes in Math 509.","DOI":"10.1007\/BFb0079307"},{"key":"ref_35","first-page":"458","article-title":"The fundamental equations of a submersion","volume":"13","year":"1966","journal-title":"Mich. Math. J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Baird, P., and Wood, J.C. (2003). Harmonic Morphism Between Riemannian Manifolds, Oxford Science Publications.","DOI":"10.1093\/acprof:oso\/9780198503620.001.0001"},{"key":"ref_37","first-page":"151","article-title":"A survey on differential geometry of Riemannian maps between Riemannian manifolds","volume":"63","author":"Sahin","year":"2017","journal-title":"Sci. Ann. Alexandru Ioan Cuza Univ. Iasi (New Ser.) Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/10\/503\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:39:24Z","timestamp":1760143164000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/10\/503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,26]]},"references-count":37,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["axioms11100503"],"URL":"https:\/\/doi.org\/10.3390\/axioms11100503","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,9,26]]}}}