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WARPED PRODUCT SEMI-SLANT SUBMANIFOLDS IN LOCALLY RIEMANNIAN PRODUCT MANIFOLDS

Published online by Cambridge University Press:  01 April 2008

MEHMET ATÇEKEN*
Affiliation:
GOP University, Faculty of Arts and Sciences, Department of Mathematics, 60200 Tokat, Turkey (email: matceken@gop.edu.tr)
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Abstract

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In this paper, we prove that there are no warped product proper semi-slant submanifolds such that the spheric submanifold of a warped product is a proper slant. But we show by means of examples the existence of warped product semi-slant submanifolds such that the totally geodesic submanifold of a warped product is a proper slant submanifold in locally Riemannian product manifolds.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Bejancu, A., ‘Semi-invariant submanifolds of locally product Riemannian manifold’, Ann. Univ. Timisoara S. Math. XXII (1984), 311.Google Scholar
[2]Cabrerizo, J. L., Carriazo, A., Fernandez, L. M. and Fernandez, M., ‘Semi-slant submanifolds of a Sasakian manifold’, Geom. Dedicata 78 (1999), 183199.CrossRefGoogle Scholar
[3]Chen, B.-Y., ‘Slant submanifolds of complex projective and complex hyperbolic spaces’, Glasg. Math. J. 42 (2000), 439454.CrossRefGoogle Scholar
[4]Chen, B.-Y., ‘Geometry of warped product CR-submanifolds in Kaehler manifolds’, Monatsh. Math. 133 (2001), 177195.CrossRefGoogle Scholar
[5]Chen, B.-Y., ‘CR-warped products in complex projective spaces with compact holomorphic factor’, Monatsh. Math. 141 (2004), 177186.CrossRefGoogle Scholar
[6]Chen, B.-Y., Geometry of slant submanifolds (Katholieke Universiteit Leuven, Leuven, 1990).Google Scholar
[7]Lotto, A., ‘Slant submanifolds in contact geometry’, Bull. Math. Soc. Roumanie 39 (1996), 183198.Google Scholar
[8]Matsumoto, K. and Mihai, I., ‘Warped product submanifolds in Sasakian space forms’, SUT J. Math. 38(2) (2002), 135144.CrossRefGoogle Scholar
[9]Matsumoto, K., ‘On submanifolds of locally product Riemannian manifolds’, TRU Math. 18(2) (1982), 145157.Google Scholar
[10]O’Neill, B., Semi-Riemannian geometry with applications to relativity (Academic Press, New York, 1983).Google Scholar
[11]Tachibana, S., ‘Some theorems on a locally product Riemannian manifold’, Tohoku Math. J. 12 (1960), 281292.CrossRefGoogle Scholar
[12]Li, H. and Li, X., ‘Semi-slant submanifolds of locally product manifold’, Georgian Math. J. 12(2) (2005), 273282.CrossRefGoogle Scholar