TY - JOUR T1 - Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds AU - Gülbahar, Mehmet AU - Trıpathı, Mukut Mani AU - Kılıç, Erol PY - 2019 DA - February Y2 - 2018 DO - 10.31801/cfsuasmas.430856 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 466 EP - 483 VL - 68 IS - 1 LA - en AB - An optimal inequality involving the scalar curvatures, the mean curvature and the k-Chen invariant is established for Riemannian submanifolds. Particular cases of this inequality is reported. Furthermore, this inequality is investigated on submanifolds, namely slant, F-invariant and F-anti invariant submanifolds of an almost constant curvature manifold. KW - Curvature KW - Riemannian submanifolds KW - almost constant curvature manifold CR - Adati, T., Submanifolds of an almost product manifold, Kodai Math. J. (1981), 4, 327-343. CR - Atçeken, M., Slant submanifolds of a Riemannian product manifold, Acta Math. Sci. Ser. B. Engl. Ed. (2010), 30(1), 215-224. CR - Bejancu, A., CR submanifolds of a Kaehler manifold I., Proc. Amer. Math. Soc. (1978), 69(1), 135-142. CR - Chen, B.-Y., A Riemannian invariant and its applications to submanifold theory, Festschrift dedicated to Katsumi Nomizu on his 70th birthday (Leuven, 1994; Brussels, 1994), Results Math. (1995), 27(1-2), 17-26. CR - Chen, B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J. (1999), 41, 33-41. CR - Chen, B.-Y., Riemannian DNA, inequalities and their applications, Tamkang J. Sci. and Eng. (2000), 3, 123-130. CR - Chen, B.-Y., Riemannian submanifolds, in Handbook of Differential Geometry, Vol. I, eds. F. Dillen and L. Verstraelen, North Holland, Amsterdam, 2000, 187-418. CR - Chen, B.-Y., On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Arch. Math. (Basel) (2000), 74, 154-160. CR - Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japan. J. Math. (N.S.) (2000), 26(1), 105-127. CR - Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and applications, World Scientific, 2011. CR - Gülbahar, M., Kılıc, E. and Saraçoglu Çelik S., Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math. (2015), 39, 884-899. CR - Kılıç, E., Tripathi, M. M. and Gülbahar, M., Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds, Ann. Polon. Math. (2016), 116(1), 37-56. CR - Liu, X. and Shao, F.-M., Skew semi-invariant submanifolds of a locally product manifold, Portugal. Math. (1999), 56(3), 319-327. CR - Sahin, B., Slant submanfiolds of an almost product Riemannian manifold, J. Korean Math. Soc. (2006), 43(4), 717-732. CR - Singer, I. M. and Thorpe, J. A., The curvature of 4-dimensional Einstein spaces, Global Analysis, Princeton University Press, 355-365, 1969. CR - Tachibana, S., Some theorems on locally product Riemannian spaces, Tohoku Math. J. (1960), 12, 281-293. CR - Tripathi, M. M., Almost semi-invariant submanifolds of a parallel ε-framed metric manifold, Ganita (1997), 48(1) 57-70. Yano, K., Differential geometry on complex and almost complex spaces, International Series of Monographs in Pure and Applied Mathematics 49. A Pergamon Press Book. The Macmillan Co., New York, 1965. CR - Yano, K., and Kon, M., Submanifolds of Kaehlerian product manifolds, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia. (1979), 15(5), 267-292. CR - Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984. UR - https://doi.org/10.31801/cfsuasmas.430856 L1 - https://dergipark.org.tr/en/download/article-file/484185 ER -