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An extrinsic look at the Riemannian Hessian

Date

Authors

Absil, P-A

Mahony, Robert

Trumpf, Jochen

Publisher

Conference Organising Committee

Abstract

Let f be a real-valued function on a Riemannian submanifold of a Euclidean space, and let f̄ be a local extension of f. We show that the Riemannian Hessian of f can be conveniently obtained from the Euclidean gradient and Hessian of f̄ by means of two m

Keywords

Keywords: Euclidean; Euclidean spaces; Orthogonal projectors; Real-valued functions; Riemannian Hessian; Shape operators; Submanifolds; Tangent space; Information science; Orthogonal functions Euclidean Hessian; Riemannian Hessian; shape operator; Weingarten map

URI

http://hdl.handle.net/1885/81197

Collections

ANU Research Publications

Source

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Type

Conference paper

DOI

10.1007/978-3-642-40020-9_39

Restricted until

2037-12-31

Downloads

File

Description

01_Absil_An_extrinsic_look_at_the_2013.pdf (166.71 KB)

02_Absil_An_extrinsic_look_at_the_2013.pdf (121.63 KB)

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