2020/02/14 by T V Mahesh, T, Mahesh, K. S. Subrahamanian Moosath +1
Mathematics · #53A15 #53C05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2002.05887
openalex publication_date 2020/02/14 · openalex created_date 2020/09/21 · openalex updated_date 2026/07/28
We show that, for an affine submersion π: M\longrightarrow B with horizontal distribution, B is a statistical manifold with the metric and connection induced from the statistical manifold M. The concept of conformal submersion with horizontal distribution is introduced, which is a generalization of affine submersion with horizontal distribution. Then proved a necessary and sufficient condition for (M, ∇, gM) to become a statistical manifold for a conformal submersion with horizontal distribution. A necessary and sufficient condition is obtained for the curve π∘ σ to be a geodesic of B, if σ is a geodesic of M for π: (M,∇) \longrightarrow (B,∇^*) a conformal submersion with horizontal distribution. Also, we obtained a necessary and sufficient condition for the tangent bundle TM to become a statistical manifold with respect to the Sasaki lift metric and the complete lift connection.