B. Y. Chen's inequalities for bi-slant submanifolds in Kenmotsu space forms

• Autorzy: Pandey P. K. , Gupta R. S. , Sharfuddin A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain B. Y. Chen's inequalities for a bi-slant submanifold M of a Kenmotsu space form M(c), when the structure vector field ξ of the ambient space is tangent to M.

Słowa kluczowe

EN

Kenmotsu space form; bi-slant submanifold; slant submanifolds; mean curvature; Chen's inequality

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 4
• Strony: 878--898
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Pandey P. K.

autor

Gupta R. S.

autor

Sharfuddin A.

• Department of Applied Mathematicsamity School of Engineering and Technology Amity University Uttar Pradesh, Noida-201303, India,

Bibliografia

• [1] A. Carriazo, A contact version of B. Y. Chen’s inequality and its applications to slant immersions, Kyungpook Math. J. 39 (1999), 465–476.
• [2] A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Sci. Math. R. S. Roumanie 39 (1996),183–198.
• [3] B. Y. Chen, A general inequality for submanifolds in complex space forms and its applications, Arch. Math. 67 (1996), 519–528.
• [4] B. Y. Chen, A Riemannian invariant and its applications to submanifold theory, Results Math. 27 (1995), 17–26.
• [5] B. Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, 1990.
• [6] B. Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math. 60 (1993), 568–578.
• [7] B. Y. Chen, F. Dillen, L. Verstraelen, L. Vrancken, An exotic totally real minimal immersion of S3 in P3 and its characterization, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 153–165.
• [8] D. Cioroboiu, B. Y. Chen inequalities for bi-slant submanifolds in Sasakian space forms, Demonstratio Math. 38 (1) (2003), 179–187.
• [9] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. Springer Verlag, Berlin- New York, 509, 1976.
• [10] D. Cioroboiu, A. Oiaga, B.Y. Chen inequalities for slant submanifolds in Sasakian space forms, Rend. Circ. Mat. Palermo (2) 52 (2003), 367–381.
• [11] F. Defever, I. Mihai, L. Verstraelen, B. Y. Chen’s inequality for C-totally real submanifolds of Sasakian space forms, Boll. Un. Mat. Ital. (7)11 (1997), 365–374.
• [12] J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J. 42 (2000), 125–138.
• [13] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math J. 21 (1972), 93–103.
• [14] M. Kobayashi, Semi-invariant submanifolds of a certain class of almost contact manifolds, Tensor (N. S.) 43 (1986), 28–36.
• [15] R. S. Gupta, I. Ahmad, S. M. K. Haider, B. Y. Chen’s inequality and its application to slant immersions into Kenmotsu manifolds, Kyungpook Math. J. 44 (1) (2004), 101–110.