manuscripta mathematica

, Volume 156, Issue 1–2, pp 241–272 | Cite as

Riemannian invariants that characterize rotational symmetries of the standard sphere

  • Masayuki AinoEmail author


Inspired by the Lichnerowicz–Obata theorem for the first eigenvalue of the Laplacian, we define a new family of invariants \(\{\Omega _k(g)\}\) for closed Riemannian manifolds. The value of \(\Omega _k(g)\) sharply reflects the spherical part of the manifold. Indeed, \(\Omega _1(g)\) and \(\Omega _2(g)\) characterize the standard sphere.

Mathematics Subject Classification

53C21 53C25 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-Ku, NagoyaJapan

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