Chen-like Inequalities on Submanifolds of Cosymplectic 3-Space Forms
Year 2023,
Volume: 13 Issue: 1&2, 89 - 109, 31.12.2023
Mehmet Gülbahar
,
Esra Erkan
Abstract
In this paper, some equalities and inequalities involving the Riemannian curvature invariants are obtained on 3-semi slant submanifolds of cosymplectic 3-space forms. Obtained relations for 3-semi slant submanifolds are examined on 3-slant, invariant, and totally real submanifolds.
References
- Kuo, Y., On almost contact 3-structure, Tôhoku Mathematical Journal (2) 22, 325–332, 1970.
- Udrişte, C., Structure presque coquaternioniennes, Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, Nouvelle Série, 13, 487– 507, 1969.
- Balgeshir, M.B.K., Point-wise slant submanifolds in almost contact geometry, Turkish Journal of Mathematics, 40, 657-664, 2006.
- Boyer, C. P., Galicki, K., 3-Sasakian manifolds, arXiv preprint hep-th/9810250, 1998.
- Galicki, K., Salamon, S., Betti numbers of 3-Sasakian manifold, Geometriae Dedicata, 63, 45-68, 1996.
- Gibbons, G.W., Rychenkova, P., Cones, tri-Sasakian structures and superconformal
invariance, Physics Letters B, 443, 138-142, 1998.
- Kashiwada, T., On a contact 3-structure, Mathematische Zeitschrift, 238, 829-832, 2001.
- Mann, B., Galicki, K., Boyer, C.P., The geometry and topology of 3-Sasakian manifolds, Journal für die. reine und angewandte Mathematik, 455, 183-220, 1994.
- Montano, B. C., De Nicola, A., 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem, Journal of Geometry and Physics, 57, 2509-2520, 2007.
- Chen, B.-Y., Geometry of slant submanifolds, Katholieke Universiteit Leuven, 1990.
- Malek, F., Balgeshir, M.B.K., Slant submanifolds of almost contact metric 3-structure manifolds, Mediterranean Journal of Mathematics, 10, 1023-1033, 2013.
- Malek, F., Balgeshir, M.B.K., Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds, Turkish Journal of Mathematics, 37, 1030-1039, 2013.
- Chen B.-Y., Mean curvature and shape operator of isometric immersions in real space forms, Glasgow Mathematical Journal, 38, 87-97, 1996.
- Chen B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Mathematical Journal, 41, 33-41, 1999.
- Chen B.-Y., Riemannian DNA, inequalities and their applications, Tamkang Journal of Science and Engineering, 3, 123-130, 2000.
- Chen B.-Y., Pseudo-Riemannian geometry, d - invariants and applications, World Scientific Publishing, 2011.
- Akgün, A., Gülbahar, M., Bi-slant submanifolds of an S manifold, Arab Journal of Mathematical Sciences, 2021.
- Li, Y., Khatri, M., Singh, J.P., Chaubey, S.K., Improved Chen’s inequalities for submanifolds of generalized Sasakian-space-forms, Axioms, 11, 324, 2022.
- Özgür, C., Chen inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection, Analele Stiintifice Ale Universitatii Al. İ. Cuza Din İasi-Serie Noua-Matematica, 58, 2012.
- Poyraz, N.Ö., Chen inequalities on spacelike hypersurfaces of a GRW spacetime, Differential Geometry and its Applications, 81, 101863, 2022.
- Poyraz, N.Ö., Doğan, B., Yaşar, E., Chen inequalities on lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection, International Electronic Journal of Geometry, 10, 1-14, 2017.
- Slesar, V., Şahin, B., Vilcu, G.E., Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms, Journal of Inequalities and Applications, 2014, 1-10, 2014.
- Siddiqui, A.N., Chen, B.Y., Bahadir, O., Statistical solitons and inequalities for statistical warped product submanifolds. Mathematics, 7, 797, 2019.
- Tripathi, M.M., Gülbahar, M., Kılıç, E., Keleş, S., Inequalities for scalar curvature of pseudo-Riemannian submanifolds, Journal of Geometry and Physics, 112, 74-84, 2017.
- Chen, B.-Y., On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Archiv der Mathematik, 74, 154-160, 2000.
- Chen B.-Y., A Riemannian invariant for submanifolds in space forms and its applications in: Geometry and Topology of Submanifolds, World Scientific Publishing, River Edge, 6, 58-81, 1994.
- Hong, S., Tripathi, M. M., On Ricci curvature of submanifolds, International Journal Pure and Applied Mathematical Sciences, 2, 227-245, 2005.
- Hong, S., Matsumoto, K., Tripathi, M.M., Certain basic inequalities for submanifolds of locally conformal Kaehler space forms, Sut Journal of Mathematics, 41, 75-94, 2005.
- Tripathi, M.M., Certain basic inequalities for submanifolds in ( k , μ ) - spaces, In: Recent Advances in Riemannian and Lorentzian Geometries (Baltimore, MD, 2003), Contemporary Mathematics 337, American Mathematical Society, 187—202, 2003.
Year 2023,
Volume: 13 Issue: 1&2, 89 - 109, 31.12.2023
Mehmet Gülbahar
,
Esra Erkan
Abstract
Bu çalışmada kosimplektik 3-uzay formlarının 3-semi slant altmanifoldları üzerine Riemann eğrilik invaryantları içeren bazı eşitlik ve eşitsizlikler elde edilmiştir. 3-semi slant alt manifoldlar için elde edilen bağıntılar, 3-slant, invaryant ve total reel altmanifoldlar üzerinde incelenmiştir.
References
- Kuo, Y., On almost contact 3-structure, Tôhoku Mathematical Journal (2) 22, 325–332, 1970.
- Udrişte, C., Structure presque coquaternioniennes, Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, Nouvelle Série, 13, 487– 507, 1969.
- Balgeshir, M.B.K., Point-wise slant submanifolds in almost contact geometry, Turkish Journal of Mathematics, 40, 657-664, 2006.
- Boyer, C. P., Galicki, K., 3-Sasakian manifolds, arXiv preprint hep-th/9810250, 1998.
- Galicki, K., Salamon, S., Betti numbers of 3-Sasakian manifold, Geometriae Dedicata, 63, 45-68, 1996.
- Gibbons, G.W., Rychenkova, P., Cones, tri-Sasakian structures and superconformal
invariance, Physics Letters B, 443, 138-142, 1998.
- Kashiwada, T., On a contact 3-structure, Mathematische Zeitschrift, 238, 829-832, 2001.
- Mann, B., Galicki, K., Boyer, C.P., The geometry and topology of 3-Sasakian manifolds, Journal für die. reine und angewandte Mathematik, 455, 183-220, 1994.
- Montano, B. C., De Nicola, A., 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem, Journal of Geometry and Physics, 57, 2509-2520, 2007.
- Chen, B.-Y., Geometry of slant submanifolds, Katholieke Universiteit Leuven, 1990.
- Malek, F., Balgeshir, M.B.K., Slant submanifolds of almost contact metric 3-structure manifolds, Mediterranean Journal of Mathematics, 10, 1023-1033, 2013.
- Malek, F., Balgeshir, M.B.K., Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds, Turkish Journal of Mathematics, 37, 1030-1039, 2013.
- Chen B.-Y., Mean curvature and shape operator of isometric immersions in real space forms, Glasgow Mathematical Journal, 38, 87-97, 1996.
- Chen B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Mathematical Journal, 41, 33-41, 1999.
- Chen B.-Y., Riemannian DNA, inequalities and their applications, Tamkang Journal of Science and Engineering, 3, 123-130, 2000.
- Chen B.-Y., Pseudo-Riemannian geometry, d - invariants and applications, World Scientific Publishing, 2011.
- Akgün, A., Gülbahar, M., Bi-slant submanifolds of an S manifold, Arab Journal of Mathematical Sciences, 2021.
- Li, Y., Khatri, M., Singh, J.P., Chaubey, S.K., Improved Chen’s inequalities for submanifolds of generalized Sasakian-space-forms, Axioms, 11, 324, 2022.
- Özgür, C., Chen inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection, Analele Stiintifice Ale Universitatii Al. İ. Cuza Din İasi-Serie Noua-Matematica, 58, 2012.
- Poyraz, N.Ö., Chen inequalities on spacelike hypersurfaces of a GRW spacetime, Differential Geometry and its Applications, 81, 101863, 2022.
- Poyraz, N.Ö., Doğan, B., Yaşar, E., Chen inequalities on lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection, International Electronic Journal of Geometry, 10, 1-14, 2017.
- Slesar, V., Şahin, B., Vilcu, G.E., Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms, Journal of Inequalities and Applications, 2014, 1-10, 2014.
- Siddiqui, A.N., Chen, B.Y., Bahadir, O., Statistical solitons and inequalities for statistical warped product submanifolds. Mathematics, 7, 797, 2019.
- Tripathi, M.M., Gülbahar, M., Kılıç, E., Keleş, S., Inequalities for scalar curvature of pseudo-Riemannian submanifolds, Journal of Geometry and Physics, 112, 74-84, 2017.
- Chen, B.-Y., On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Archiv der Mathematik, 74, 154-160, 2000.
- Chen B.-Y., A Riemannian invariant for submanifolds in space forms and its applications in: Geometry and Topology of Submanifolds, World Scientific Publishing, River Edge, 6, 58-81, 1994.
- Hong, S., Tripathi, M. M., On Ricci curvature of submanifolds, International Journal Pure and Applied Mathematical Sciences, 2, 227-245, 2005.
- Hong, S., Matsumoto, K., Tripathi, M.M., Certain basic inequalities for submanifolds of locally conformal Kaehler space forms, Sut Journal of Mathematics, 41, 75-94, 2005.
- Tripathi, M.M., Certain basic inequalities for submanifolds in ( k , μ ) - spaces, In: Recent Advances in Riemannian and Lorentzian Geometries (Baltimore, MD, 2003), Contemporary Mathematics 337, American Mathematical Society, 187—202, 2003.