Doubly autoparallel structure and curvature integrals

Author:

Ohara AtsumiORCID,Ishi Hideyuki,Tsuchiya Takashi

Abstract

AbstractOn a statistical manifold, we can define autoparallel submanifolds and path integrals of the second fundamental forms (curvature integrals) for its primal and dual affine connections, respectively. A submanifold is called doubly autoparallel if it is simultaneously autoparallel with respect to the both connections. In this paper we first discuss common properties of such submanifolds. In particular we next give an algebraic characterization of them in Jordan algebras and show their applications. Further, we exhibit that both curvature integrals induced from dually flat structure are interestingly related to an unexpected quantity, i.e., iteration-complexity of the interior-point algorithms for convex optimization defined on a submanifold that is not doubly autoparallel.

Funder

JSPS

MEXT Promotion of Distinctive Joint Reseach Center

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Theory and Mathematics,Computer Science Applications,Geometry and Topology,Statistics and Probability

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