The exponential map of a -metric

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• 作者：Michael Kunzinger ; ^{michael.kunzinger@univie.ac.at" class="auth_mail} ; Roland Steinbauer ^{roland.steinbauer@univie.ac.at" class="auth_mail} ; Milena Stojkovi膰 ^{milena.stojkovic@live.com" class="auth_mail}
• 关键词：53B20 ; 53B21 ; 53B30
• 刊名：Differential Geometry and its Applications
• 出版年：June 2014
• 年：2014
• 卷：34
• 期：Complete
• 页码：14-24
• 全文大小：292 K

文摘

Given a pseudo-Riemannian metric of regularity mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224514000370&_mathId=si1.gif&_user=111111111&_pii=S0926224514000370&_rdoc=1&_issn=09262245&md5=38b09c3d1b4436ef86efc7a71facb132" title="Click to view the MathML source">C^1,1mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><msup><mrow><mi>Cmi>mrow><mrow><mn>1mn><mo>,mo><mn>1mn>mrow>msup>math> on a smooth manifold, we prove that the corresponding exponential map is a bi-Lipschitz homeomorphism locally around any point. We also establish the existence of totally normal neighborhoods in an appropriate sense. The proofs are based on regularization, combined with methods from comparison geometry.