B. Y. Chen’s Inequalities for Bi-slant Submanifolds in Cosymplectic Space Forms
DOI:
https://doi.org/10.5644/SJM.09.1.11Keywords:
Cosymplectic space form, bi-slant submanifold, slant submanifolds, mean curvature, Chen’s inequalityAbstract
In this paper we obtain B. Y. Chen's inequalities for a bi-slant submanifold {M} of a cosymplectic space form $\overline{M}$(c), when the structure vector field $\xi$ of the ambient space is tangent to $M$.
2000 Mathematics Subject Classification. 53C40, 53B25, 53D15
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References
A. Carriazo: A contact version of B. Y. Chen’s inequality and its applications to slant immersions, Kyungpook Math., J. 39 (1999), 465–476.
A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie, 39 (1996),183-198.
B. Y. Chen, A general inequality for submanifolds in complex space forms and its applications, Arch. Math., 67 (1996), 519–528.
B. Y. Chen, A Riemannian invariant and its applications to submanifold theory, Result. Math., 27 (1995), 17–26.
B. Y. Chen, Geometry of Slant Submanifolds, Katholieke universiteit Leuven, 1990.
B. Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math., 60 (1993), 568–578.
B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, An exotic totally real minimal immersion of $S^{3}$ in $P^{3}$ and its characterization, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 153–165.
D. Cioroboiu, B. Y. Chen inequalities for bi-slant submanifolds in sasakian space forms, Demonstratio Math., 38 (1) (2003), 179–187.
D. E. Blair, Contact Manifolds in Riemannian Geometry, Lect. Notes in Math. Springer Verlag, Berlin- New York, 509, 1976.
D. Cioroboiu abd A. Oiaga, B.Y. Chen inequalities for slant submanifolds in Sasakian space forms, Rend. Circ. Sem. Mat. Palermo, 52 (2) (2003), 367–381.
F. Defever, I. Mihai, and L. Verstraelen, B. Y. Chens inequality for C-totally real submanifolds of Sasakian space forms, Bollettino U. M. I., 11 (7) (1997), 365–374.
J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J., 42 (2000), 125–138.
G. D. Ludden, Submanifolds of cosymplectic manifolds, J. Differ. Geom., 4 (1970), 237–244.
M. Kobayashi, Semi-invariant submanifolds of a certain class of almost contact manifolds, Tensor (N. S.), 43 (1986), 28–36.
Ram Shankar Gupta, S. M. Khursheed Haider and M. H. Sahid, Slant submanifolds of cosymplectic manifolds, An. St. Univ. AI. I. Cuza, 50 (1) (2004), 33–49.