Contact CR-warped product submanifolds in generalized Sasakian space forms

We consider a contact CR-warped product submanifold M=M\top \timesfM\bot of a trans-Sasakian generalized Sasakian space form \widetilde{M} (f1,f2,f3). We show that M is a contact CR-product under certain conditions.

Anahtar Kelimeler:

Warped product manifold, contact CR-warped product submanifold, trans-Sasakian manifold, generalized Sasakian space form

Contact CR-warped product submanifolds in generalized Sasakian space forms

Keywords:

Warped product manifold, contact CR-warped product submanifold, trans-Sasakian manifold, generalized Sasakian space form,

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Arslan, K., Ezenta¸s, R., Mihai, I., Murathan, C.: Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc. 42, 1101–1110 (2005).
At¸ceken, M.: Contact CR-warped product submanifolds in cosymplectic space forms, to appear in Collect. Math. Blair, D. E.: Contact manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin, 1976.
Chen, B. Y.: Geometry of submanifolds and its applications, Science University of Tokyo, Tokyo, 1981.
Chen, B. Y.: Geometry of warped product CR-submanifolds in Kaehler manifold, Monatsh. Math. 133, 177–195 (2001).
Chen, B. Y.: Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math. 134, 103–119 (2001).
Hasegawa, I., Mihai, I.: Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102, –150 (2003).
Kenmotsu, K.: A class of almost contact Riemannian manifolds, Tˆohoku Mathematical Journal 24, 93–103 (1972).
Ludden, G. D.: Submanifolds of cosymplectic manifolds, Journal of Diﬀerential Geometry 4, 237–244 (1970).
Mihai, I.: Contact CR-warped product submanifolds in Sasakian space forms, Geom. Dedicata, 109, 165–173, (2004).
O’Neill, B.: Semi-Riemannian geometry with applications to relativity, Academic Press, N-Y, London 1983.
Oubina, J. A.: New classes of almost contact metric structures, Publications Mathematicae Debrecen 32, 187–193 (1985).
Sibel SULAR, Cihan ¨OZG ¨UR Department of Mathematics, Balıkesir University, , Balıkesir-TURKEY e-mails: csibel@balikesir.edu.tr, cozgur@balikesir.edu.tr