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A Topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere

  • Fulya Şahin and Bayram Şahin EMAIL logo
Published/Copyright: June 11, 2022
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 72 Issue 3

Abstract

In this paper, we investigate topological sphere theorems for compact minimal contact CR-submanifolds of odd dimensional unit sphere. We show that if an inequality involving the warping function and the scalar curvature of the fibers is satisfied, a compact minimal contact CR-warped product submanifold of the odd dimensional unit sphere is homeomorphic to the sphere. In particular case, for 5-dimensional unit sphere, we show that a 4-dimensional compact minimal contact CR-warped product submanifold is homeomorphic to a sphere if ∣∇ln f∣2 < 1 is satisfied. By using Bonnet-Myers’s theorem we give a result about fundamental group and by Leung’s theorem we obtain a result about homology groups of a contact CR-warped submanifold.

Keywords: Contact CR-warped submanifold; Sphere theorem; homology group
MSC 2010: Primary 55N25; 53C65; 53C40; 53C15

This work was supported by Research Fund of the Ege University Grant No.20776.

bayram.sahin@ege.edu.tr

  1. (Communicated by Július Korbaš)

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Received: 2021-04-03
Accepted: 2021-06-08
Published Online: 2022-06-11
Published in Print: 2022-06-27

© 2022 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2022-0050
Keywords for this article
Contact CR-warped submanifold; Sphere theorem; homology group

Articles in the same Issue

  1. Regular Papers
  2. The poset of morphism-extension classes of countable graphs
  3. Characterization of monadic BL-algebras by state operators
  4. Comments on efficient batch verification test for digital signatures based on elliptic curves
  5. On necessary and sufficient conditions for the monogeneity of a certain class of polynomials
  6. An exponential Diophantine equation involving the sum or difference of powers of two Pell numbers
  7. Some results on certain types of Putcha semigroups
  8. Inner functions in QK spaces and multipliers
  9. Certain subclasses of meromorphic multivalent q-starlike and q-convex functions
  10. Algebraic dependences of meromorphic mappings into a projective space sharing few hyperplanes
  11. Unbounded oscillation criteria for fourth order neutral differential equations of non-canonical type
  12. Existence of radial solutions for a weighted p-biharmonic problem with navier boundary condition on the Heisenberg group
  13. Intuitionistic fuzzy Tribonacci I-convergent sequence spaces
  14. Lipschitz class functions and their general Fourier coefficients
  15. Spectra and fine spectra of the generalized upper difference operator with triple repetition Δ3ab on the Hahn sequence space
  16. A Topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere
  17. An extended type I half-logistic family of distributions: Properties, applications and different method of estimations
  18. On the Unit-Chen distribution with associated quantile regression and applications
  19. A note on Lévy subordinators in cones of fuzzy sets in Banach spaces
  20. Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors
  21. Upper bound for variance of finite mixtures of power exponential distributions
  22. The dimension Dind of finite topological T0-spaces
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