Conformal anti-invariant riemannian maps to KÄhler manifolds

Akyol M. A., Şahin B.

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, vol.80, no.4, pp.187-198, 2018 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 80 Issue: 4
  • Publication Date: 2018
  • Journal Name: UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.187-198
  • Keywords: Anti-invariant riemannian map, Anti-invariant submanifold, Conformal anti-invariant riemannian map, Harmonic map, Totally geodesic map
  • Uşak University Affiliated: No

Abstract

We introduce conformal anti-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds and show that they include both anti-invariant submanifolds and anti-invariant Riemannian maps. We give non-trivial examples, investigate the geometry of certain distributions and obtain decomposition theorems for the base manifold. The harmonicity and totally geodesicity of conformal anti-invariant Riemannian maps are also obtained. Moreover, we study weakly umbilical conformal Riemannian maps and obtain a classification theorem for umbilical conformal anti-invariant Riemannian maps.