多様体のモース指数　2025年10月2日現地刊行予定

Morse Index of Minimal Submanifolds '25

[著者]Urbano, Francisco

（翻訳和名　極小部分多様体のモース指数）

[出版社] American Mathematical Society
[出版年月日] 2025/10
[ISBN-10] 1470480212
[ISBN-13] 978-1-4704-8021-9
[出版国] アメリカ合衆国
[装丁] paper/Kt./br.
[媒体] 冊子
[ページ数] 308 p.

本書は、リーマン多様体の極小部分多様体のモース指数に関する主要な結果を体系的に扱う。

This book provides a systematic treatment of the main results on the Morse index of minimal submanifolds of Riemannian manifolds. After an introductory chapter reviewing the necessary material, this book provides a survey of the basic properties of the Morse index, as well as a large number of examples of minimal submanifolds with the corresponding calculation of their Morse index. The analysis of minimal submanifolds and their index in the cases when the ambient manifold is the Euclidean space, sphere, real and complex projective spaces are analyzed in detail; many other classes of ambient varieties are also studied. The text also includes some of the main open problems in the theory. Potential readers of this book are graduate students and researchers in geometric analysis.

This book is published in cooperation with Real Sociedad Matematica Espanola.

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