INVARIANT AND ANTI-INVARIANT RIEMANNIAN MAPS TO KAHLER MANIFOLDS


Sahin B.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.7, no.3, pp.337-355, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1142/s0219887810004324
  • Title of Journal : INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Page Numbers: pp.337-355

Abstract

As a generalization of isometric immersions and Riemannian submersions, Riemannian maps were introduced by Fischer [Riemannian maps between Riemannian manifolds, Contemp. Math. 132 (1992) 331-366]. It is known that a real valued Riemannian map satisfies the eikonal equation which provides a bridge between physical optics and geometrical optics. In this paper, we introduce invariant and anti-invariant Riemannian maps between Riemannian manifolds and almost Hermitian manifolds as a generalization of invariant immersions and totally real immersions, respectively. Then we give examples, present a characterization and obtain a geometric characterization of harmonic invariant Riemannian maps in terms of the distributions which are involved in the definition of such maps. We also give a decomposition theorem by using the existence of invariant Riemannian maps to Kahler manifolds. Moreover, we study anti-invariant Riemannian maps, give examples and obtain a classification theorem for umbilical anti-invariant Riemannian maps.