INVARIANT AND ANTI-INVARIANT RIEMANNIAN MAPS TO KAHLER MANIFOLDS


Sahin B.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.7, ss.337-355, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 7 Konu: 3
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1142/s0219887810004324
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Sayfa Sayıları: ss.337-355

Özet

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.