Totally geodesic submanifolds of symmetric spaces, III

2013/07/28 by Chen, Bang-Yen, Leung, Pui-Fai, Nagano, Tadashi
#Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1307.7325

Abstract

One purpose of this article is to establish a general method to determine stability of totally geodesic submanifolds of symmetric spaces. The method is used to determine the stability of the basic totally geodesic submanifolds M₊,M_- introduced and studied by Chen and Nagano in [Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978), 405--425] as minimal submanifolds. The other purpose is to establish a stability theorem for minimal totally real submanifolds of Kählerian manifolds.

Related

• Totally geodesic submanifolds in Riemannian symmetric spaces
• Maximal totally geodesic submanifolds and index of symmetric spaces
• Rigidity and stability estimates for minimal submanifolds in the hyperbolic space
• Totally geodesic submanifolds in exceptional symmetric spaces
• A class of complete embedded minimal submanifolds in noncompact symmetric spaces