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Submanifolds of F -structure manifold satisfying F K + ( − ) K + 1 F = 0

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  • Lovejoy S. Das

Abstract

The purpose of this paper is to study invariant submanifolds of an n -dimensional manifold M endowed with an F -structure satisfying F K + ( − ) K + 1 F = 0 and F W + ( − ) W + 1 F ≠ 0 for 1 < W < K , where K is a fixed positive integer greater than 2 . The case when K is odd ( ≥ 3 ) has been considered in this paper. We show that an invariant submanifold M ˜ , embedded in an F -structure manifold M in such a way that the complementary distribution D m is never tangential to the invariant submanifold ψ ( M ˜ ) , is an almost complex manifold with the induced F ˜ -structure. Some theorems regarding the integrability conditions of induced F ˜ -structure are proved.

Suggested Citation

  • Lovejoy S. Das, 2001. "Submanifolds of F -structure manifold satisfying F K + ( − ) K + 1 F = 0," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 26, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:643279
    DOI: 10.1155/S0161171201005257
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