Heliyon (Sep 2024)

Homology groups in CR-warped products of complex space forms

  • Yanlin Li,
  • Akram Ali,
  • Nadia Alluhaibi,
  • Fatemah Mofarreh,
  • Cenap Ozel

Journal volume & issue
Vol. 10, no. 17
p. e36772

Abstract

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In the present paper, by using the result of Lawson-Simons [15], we adopt a different technique to show that there are no stable integral q-currents and a non-trivial homology group in a compact oriented CR-warped product submanifold Nn in a complex space forms space Qcm(4c) by imposing some restrictions on the squared norm of gradient and the Laplacian of warped function. Finally, we show that the same approach can be given by using Dirichlet energy, positive eigenvalue, and Hamiltonian.

Keywords