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On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature

Author

Listed:
  • Yanlin Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
    These authors contributed equally to this work.)

  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • Akram Ali

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • Pişcoran Laurian-Ioan

    (Department of Mathematics and Computer Science, North University Center of Baia Mare, Technical University of Cluj Napoca, 430122 Baia Mare, Romania)

Abstract

In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form Ω n = N T l × f N ϕ k in a complex projective space C P 2 m ( 4 ) . Additionally, we will find certain restrictions on the warping function f , Dirichlet energy function E ( f ) , and first non-zero eigenvalue λ 1 to prove that stable l -currents do not exist and also that the homology groups have vanished in Ω n . As an application of the non-existence of the stable currents in Ω n , we show that the fundamental group π 1 ( Ω n ) is trivial and Ω n is simply connected under the same extrinsic conditions. Further, some similar conclusions are provided for CR-warped product submanifolds.

Suggested Citation

  • Yanlin Li & Ali H. Alkhaldi & Akram Ali & Pişcoran Laurian-Ioan, 2021. "On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3156-:d:697369
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