Isotropic submanifolds of pseudo-Riemannian spaces

• Published in: Journal of geometry and physics Vol. 62; no. 9; pp. 1915 - 1924
• Main Authors: Cabrerizo, J.L., Fernández, M., Gómez, J.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2012
• Subjects: Isometric immersion; Isotropic submanifold; Lorentzian submanifold; Pseudo-Riemannian manifold; Spacelike submanifold; Spacelike submanifold; Isotropic submanifold; 53C40; Isometric immersion; Lorentzian submanifold; Pseudo-Riemannian manifold; 53C25
• ISSN: 0393-0440; 1879-1662
• DOI: 10.1016/j.geomphys.2012.05.002

The family of all the submanifolds of a given Riemannian or pseudo-Riemannian manifold is large enough to classify them into some interesting subfamilies such as minimal (maximal), totally geodesic, Einstein, etc. Most of these have been extensively studied by many authors, but as far as we know, no paper has hitherto been published on the class of isotropic submanifolds. The purpose of this paper is therefore to gain a better understanding of this interesting class of submanifolds that arise naturally in mathematics and physics by studying their relationships with other closely distinguished families.