Chen-like Inequalities on Submanifolds of Cosymplectic 3-Space Forms

Öz

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.

Anahtar Kelimeler

• Curvature
• Submanifold
• Cosymplectic 3-Space Form

Öz

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.

Anahtar Kelimeler

• Eğrilik
• Altmanifold
• Kosimplektik 3-Uzay Form

Kaynakça

1. Kuo, Y., On almost contact 3-structure, Tôhoku Mathematical Journal (2) 22, 325–332, 1970.
2. 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.
3. Balgeshir, M.B.K., Point-wise slant submanifolds in almost contact geometry, Turkish Journal of Mathematics, 40, 657-664, 2006.
4. Boyer, C. P., Galicki, K., 3-Sasakian manifolds, arXiv preprint hep-th/9810250, 1998.
5. Galicki, K., Salamon, S., Betti numbers of 3-Sasakian manifold, Geometriae Dedicata, 63, 45-68, 1996.
6. Gibbons, G.W., Rychenkova, P., Cones, tri-Sasakian structures and superconformal invariance, Physics Letters B, 443, 138-142, 1998.
7. Kashiwada, T., On a contact 3-structure, Mathematische Zeitschrift, 238, 829-832, 2001.
8. 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.

9. Montano, B. C., De Nicola, A., 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem, Journal of Geometry and Physics, 57, 2509-2520, 2007.
10. Chen, B.-Y., Geometry of slant submanifolds, Katholieke Universiteit Leuven, 1990.
11. Malek, F., Balgeshir, M.B.K., Slant submanifolds of almost contact metric 3-structure manifolds, Mediterranean Journal of Mathematics, 10, 1023-1033, 2013.
12. 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.
13. Chen B.-Y., Mean curvature and shape operator of isometric immersions in real space forms, Glasgow Mathematical Journal, 38, 87-97, 1996.
14. Chen B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Mathematical Journal, 41, 33-41, 1999.
15. Chen B.-Y., Riemannian DNA, inequalities and their applications, Tamkang Journal of Science and Engineering, 3, 123-130, 2000.
16. Chen B.-Y., Pseudo-Riemannian geometry, d - invariants and applications, World Scientific Publishing, 2011.
17. Akgün, A., Gülbahar, M., Bi-slant submanifolds of an S manifold, Arab Journal of Mathematical Sciences, 2021.
18. 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.
19. 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.
20. Poyraz, N.Ö., Chen inequalities on spacelike hypersurfaces of a GRW spacetime, Differential Geometry and its Applications, 81, 101863, 2022.
21. 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.
22. 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.
23. Siddiqui, A.N., Chen, B.Y., Bahadir, O., Statistical solitons and inequalities for statistical warped product submanifolds. Mathematics, 7, 797, 2019.
24. 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.
25. Chen, B.-Y., On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Archiv der Mathematik, 74, 154-160, 2000.
26. 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.
27. Hong, S., Tripathi, M. M., On Ricci curvature of submanifolds, International Journal Pure and Applied Mathematical Sciences, 2, 227-245, 2005.
28. 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.
29. 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.