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WARPED PRODUCT SEMI-SLANT SUBMANIFOLDS IN LOCALLY RIEMANNIAN PRODUCT MANIFOLDS

  • MEHMET ATÇEKEN (a1)
Abstract
Abstract

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.

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[2]J. L. Cabrerizo , A. Carriazo , L. M. Fernandez and M. Fernandez , ‘Semi-slant submanifolds of a Sasakian manifold’, Geom. Dedicata 78 (1999), 183199.

[3]B.-Y. Chen , ‘Slant submanifolds of complex projective and complex hyperbolic spaces’, Glasg. Math. J. 42 (2000), 439454.

[4]B.-Y. Chen , ‘Geometry of warped product CR-submanifolds in Kaehler manifolds’, Monatsh. Math. 133 (2001), 177195.

[5]B.-Y. Chen , ‘CR-warped products in complex projective spaces with compact holomorphic factor’, Monatsh. Math. 141 (2004), 177186.

[6]B.-Y. Chen , Geometry of slant submanifolds (Katholieke Universiteit Leuven, Leuven, 1990).

[11]S. Tachibana , ‘Some theorems on a locally product Riemannian manifold’, Tohoku Math. J. 12 (1960), 281292.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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