{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:39:07Z","timestamp":1760060347788,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T00:00:00Z","timestamp":1755820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Innovations and Technological Development of Serbia","award":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"],"award-info":[{"award-number":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"]}]},{"name":"Faculty of Teacher Education, Leposavi\u0107","award":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"],"award-info":[{"award-number":["451-03-137\/2025-03\/200251","451-03-137\/2025-03\/200102","IMP-003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Conformal mappings between Riemannian spaces R\u00afN and RN are defined by the explicit transformation of the metric tensor of the space R\u00afN to the metric tensor of the space RN. Geodesic mapping between these two Riemannian spaces is a transformation that transforms any geodesic line of the space R\u00afN to a geodesic line of the space RN. In this research, we defined an m-conformal line of a Riemannian space, which is geodesic if m=0. Based on this definition, we involved the concept of (m\u00af,m)-conformal mapping as a transformation R\u00afN\u2192RN in which any m\u00af-conformal line of the space R\u00afN transforms to an m-conformal line of the space RN. The result of this research is the establishment of three invariants for these mappings. At the end of this research, we gave an example of a scalar geometrical object which may be used in physics.<\/jats:p>","DOI":"10.3390\/axioms14090652","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T13:47:49Z","timestamp":1755870469000},"page":"652","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On (m\u00af, m)-Conformal Mappings"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0643-0955","authenticated-orcid":false,"given":"Branislav M.","family":"Randjelovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Electronic Engineering, University of Ni\u0161, 18000 Ni\u0161, Serbia"},{"name":"Faculty of Teachers Education, University of K. Mitrovica, 38218 Leposavi\u0107, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1709-0765","authenticated-orcid":false,"given":"Du\u0161an J.","family":"Simjanovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Belgrade Metropolitan University, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7598-9058","authenticated-orcid":false,"given":"Nenad O.","family":"Vesi\u0107","sequence":"additional","affiliation":[{"name":"Mathematical Institute of Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9414-0711","authenticated-orcid":false,"given":"Ivana","family":"Djuri\u0161i\u0107","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Research, University of Belgrade, 11000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8965-1480","authenticated-orcid":false,"given":"Branislav D.","family":"Vlahovi\u0107","sequence":"additional","affiliation":[{"name":"Department of Physics, North Carolina Central University, Durham, NC 27707, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"ref_1","unstructured":"Eisenhart, L.P. (1947). Riemannian Geometry, Princeton University Press."},{"key":"ref_2","unstructured":"Mike\u0161, J. (2015). Differential Geometry of Special Mappings, Olomouc University Press. [1st ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Shandra, I.G., and Mike\u0161, J. (2019). Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields. Mathematics, 7.","DOI":"10.3390\/math7080692"},{"key":"ref_4","first-page":"21","article-title":"On special almost geodesic mappings of type \u03c01 of spaces with affine connection","volume":"43","author":"Berezovsky","year":"2004","journal-title":"Acta Univ. Palacki. Olomuc. Fac. Rerum Natur. Math."},{"key":"ref_5","first-page":"389","article-title":"Conformally geodesic mappings satisfying a certain initial condition","volume":"47","author":"Chuda","year":"2011","journal-title":"Arch. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/BF02365193","article-title":"Geodesic mappings of affine-connected and Riemannian spaces","volume":"78","year":"1996","journal-title":"J. Math. Sci."},{"key":"ref_7","first-page":"74","article-title":"Some actual aspects of development of the theory of geodesic mappings of Riemannian spaces and its generalization","volume":"38","author":"Sinyukov","year":"1994","journal-title":"Rus. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/BF01141945","article-title":"Holomorphically projective mappings of special K\u00e4hler spaces","volume":"36","author":"Sinyukov","year":"1984","journal-title":"Math. Notes"},{"key":"ref_9","unstructured":"Sinyukov, N.S. (1979). Geodesic Mappings of Riemannian Spaces, Nauka. [1st ed.]."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"826","DOI":"10.31801\/cfsuasmas.1172289","article-title":"Characterization of a paraSasakian manifold admitting Bach tensor","volume":"72","author":"De","year":"2023","journal-title":"Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"032501","DOI":"10.1063\/5.0033967","article-title":"Perfect fluid spacetimes and Yamabe solitons","volume":"62","author":"De","year":"2021","journal-title":"J. Math. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Milenkovi\u0107, V.M., Stankovi\u0107, M.S., and Vesi\u0107, N.O. (2025). Invariant Geometric Objects of the Equitorsion Canonical Biholomorphically Projective Mappings of Generalized Riemannian Space in the Eisenhart Sense. Mathematics, 13.","DOI":"10.3390\/math13081334"},{"key":"ref_13","first-page":"195","article-title":"On holomorphically projective mappings of generalized Kahlerian spaces","volume":"54","year":"2002","journal-title":"Mat. Vesn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"77","DOI":"10.4171\/rsmup\/124-5","article-title":"On equitorsion geodesic mappings of general affine connection spaces","volume":"124","year":"2010","journal-title":"Rend. Sem. Mat. Univ. Padova"},{"key":"ref_15","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.","DOI":"10.3390\/axioms11050239"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4581","DOI":"10.1007\/s00009-016-0763-z","article-title":"Some Invariants of Equitorsion Third Type Almost Geodesic Mappings","volume":"13","year":"2016","journal-title":"Mediterr. J. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"463","DOI":"10.2298\/FIL1403463Z","article-title":"On equitorsion concircular tensors of generalized Riemannian spaces","volume":"28","author":"Hinterleitner","year":"2014","journal-title":"Filomat"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00009-022-02119-x","article-title":"Einstein Type Curvature Tensors and Einstein Type Tensors of Generalized Riemannian Space in the Eisenhart Sense","volume":"19","year":"2022","journal-title":"Mediterr. J. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3927","DOI":"10.2298\/FIL2312927Z","article-title":"Quarter-symmetric generalized metric connections on a generalized Riemannian manifold","volume":"37","year":"2023","journal-title":"Filomat"},{"key":"ref_20","first-page":"149","article-title":"Geodesic infinitesimal deformations of generalized Riemannian spaces","volume":"19","year":"2022","journal-title":"Mediterr. J. Math."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.1142\/S0217732309032046","article-title":"On the significance of the Weyl curvature in a relativistic cosmological model","volume":"24","author":"Danehkar","year":"2009","journal-title":"Mod. Phys. Let. A"},{"key":"ref_23","first-page":"3453","article-title":"The Canonical Structure of the First-Order Einstein-Hilbert Action","volume":"25","author":"McKeon","year":"2010","journal-title":"Phys. Rev. A."},{"key":"ref_24","unstructured":"Dodelson, S. (2003). Modern Cosmology, Elsevier. [1st ed.]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/9\/652\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:34:12Z","timestamp":1760034852000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/9\/652"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,22]]},"references-count":24,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["axioms14090652"],"URL":"https:\/\/doi.org\/10.3390\/axioms14090652","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,8,22]]}}}