The second variational formula of the variational problems for mappings between statistical manifolds

2025/07/18 by Urakawa, Hajime
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.13612

Abstract

Recently, H. Furuhata and R. Ueno obtained the first variational formula of smooth mappings of a compact statistical manifold into another manifold. In this paper, we show the second variational formula of harmonic mappings of a statistical manifold into another one. Furthermore, we define the stability, the index and the nullity for the mappings, and we show the weakly stability for the harmonic mappings into any statistical manifolds of non-positive curvature. We also give several examples calculating the indexes and nullities.

Citations

• A Variation Problem for Mappings between Statistical Manifolds
• Classification theorems for biharmonic real hypersurfaces in a complex projective space
• Biharmonic orbits of isotropy representations of symmetric spaces
• Biharmonic maps into a Riemannian manifold of non-positive curvature
• On the generalized Chen's conjecture on biharmonic submanifolds
• Classifications and Isolation Phenomena of Bi-Harmonic Maps and Bi-Yang-Mills Fields
• On the biharmonic and harmonic indices of the Hopf map

Related

• The Second Variational Formula for Statistical Biharmonic Maps
• A Variation Problem for Mappings between Statistical Manifolds
• The second variational formula of the k-energy and k-harmonic curves
• Geometry of k-harmonic maps and the second variational formula of the k-energy
• On stability of exponentially subelliptic harmonic maps