Bulletin of the Australian Mathematical Society

Research Article

WARPED PRODUCT SEMI-SLANT SUBMANIFOLDS IN LOCALLY RIEMANNIAN PRODUCT MANIFOLDS

MEHMET ATÇEKENa1

a1 GOP University, Faculty of Arts and Sciences, Department of Mathematics, 60200 Tokat, Turkey (email: matceken@gop.edu.tr)

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.

(Received March 27 2007)

2000 Mathematics subject classification

  • 53C15;
  • 53C40

Keywords and phrases

  • warped product;
  • slant distribution;
  • semi-slant submanifold;
  • spheric foliation and locally Riemannian product manifold