{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:16:26Z","timestamp":1760145386716,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T00:00:00Z","timestamp":1720483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technological Development","award":["451-03-65\/2024-03\/200102","451-03-65\/2024-03\/200251"],"award-info":[{"award-number":["451-03-65\/2024-03\/200102","451-03-65\/2024-03\/200251"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications in physics.<\/jats:p>","DOI":"10.3390\/axioms13070463","type":"journal-article","created":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T15:27:20Z","timestamp":1720538840000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Special Geometric Objects in Generalized Riemannian Spaces"],"prefix":"10.3390","volume":"13","author":[{"given":"Marko","family":"Stefanovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, 18000 Ni\u0161, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nenad","family":"Vesi\u0107","sequence":"additional","affiliation":[{"name":"Mathematical Institute of Serbian Academy of Sciences and Arts, University of Belgrade, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1709-0765","authenticated-orcid":false,"given":"Du\u0161an","family":"Simjanovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Metropolitan University, 11158 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0643-0955","authenticated-orcid":false,"given":"Branislav","family":"Randjelovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Electronic Engineering, University of Ni\u0161, 18000 Ni\u0161, Serbia"},{"name":"Faculty of Teachers Education, University of Pri\u0161tina in K. 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Quantum Gravity"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"025002","DOI":"10.1088\/1361-6382\/ab5cc3","article-title":"Non-symmetric Riemannian gravity and Sasaki-Einstein 5-manifolds","volume":"37","author":"Ivanov","year":"2020","journal-title":"Class. Quantum Gravity"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"20989","DOI":"10.3934\/math.20231068","article-title":"A fixed point theorem in strictly convex b-fuzzy metric spaces","volume":"8","author":"Cirovic","year":"2023","journal-title":"AIMS Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"233","DOI":"10.2298\/AADM200911057R","article-title":"A Characterisation of Completeness of B-Fuzzy Metric Spaces and Nonlinear Contractions","volume":"15","year":"2021","journal-title":"Appl. Anal. Discret. Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"961","DOI":"10.18514\/MMN.2021.3482","article-title":"Novel Invariants for Almost Geodesic Mappings of the Third Type","volume":"22","year":"2021","journal-title":"Miskolc Math. Notes"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"473","DOI":"10.18514\/MMN.2020.2901","article-title":"Basic Invariants of Geometric Mappings","volume":"21","year":"2020","journal-title":"Miskolc Math. Notes"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1073\/pnas.11.4.199","article-title":"On the projective and equi-projective geometries of paths","volume":"11","author":"Thomas","year":"1925","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_21","first-page":"99","article-title":"Zur infinitesimal geometrie: Einordnung der projectiven und der konformen auffssung","volume":"11","author":"Weyl","year":"1921","journal-title":"Gott. Nachrichten"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"439","DOI":"10.2298\/FIL1203439S","article-title":"Geodesic mappings of equiaffine and anti-equiaffine general affine connection spaces preserving torsion","volume":"26","year":"2012","journal-title":"Filomat"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"77","DOI":"10.4171\/rsmup\/124-5","article-title":"On Equitorsion Geodesic Mappings of General Affine Connection Space","volume":"124","year":"2010","journal-title":"Rend. Semin. Mat. \u2019Universita\u2019 Padova\/Math. J. Univ. Padova"},{"key":"ref_24","first-page":"26","article-title":"Equitorsion Holomorphically Projective Mappings of Generalized K\u00e4hlerian Space of the Second Kind","volume":"3","year":"2010","journal-title":"Int. Electron. J. Geom."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1016\/j.aml.2011.10.045","article-title":"New projective tensors for equitorsion geodesic mappings","volume":"25","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/j.jmaa.2017.09.021","article-title":"Some invariants of holomorphically projective mappings of generalized K\u00e4hlerian spaces","volume":"458","year":"2018","journal-title":"J. Math. Anal. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"71","DOI":"10.2298\/PIM1512071N","article-title":"Conformal and Geodesic Mappings of Generalized Equidistant Spaces","volume":"98","author":"Hinterleitner","year":"2015","journal-title":"Publ. Inst. Math."},{"doi-asserted-by":"crossref","unstructured":"Vesi\u0107, N.O., Milenkovi\u0107, V.M., and Stankovi\u0107, M.S. (2022). Two Invariants for Geometric Mappings. Axioms, 11.","key":"ref_28","DOI":"10.3390\/axioms11050239"},{"unstructured":"Silverman, R.A. (1963). Calculus of Variations, Prentice-Hall, Inc.. Revised English Edition.","key":"ref_29"},{"unstructured":"Blau, M. (2015). Lecture Notes on General Relativity, Albert Einstein Center for Fundamental Physics, Universit\u00e4t Bern.","key":"ref_30"},{"unstructured":"Sean, C.M. (2004). Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley.","key":"ref_31"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1088\/0264-9381\/5\/4\/010","article-title":"Scalar Fields Curved Spacetimes","volume":"5","author":"Madsen","year":"1988","journal-title":"Class. Quantum Gravity"},{"key":"ref_33","first-page":"1519","article-title":"Generalized Riemannian Spaces With Respect to 4-Velocity Vectors and Functions of State Parameters","volume":"35","year":"2020","journal-title":"Filomat"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1103\/RevModPhys.48.393","article-title":"General relativity with spin and torison: Foundations and prospects","volume":"48","author":"Hehl","year":"1976","journal-title":"Rev. Mod. 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