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Lectures on n-Sasakian Manifolds

Part of the Lecture Notes in Mathematics book series (LNM,volume 2110)

Abstract

These notes grew from a series of four 90 min lectures given at CIMAT in Guanajuato, Mexico in December 2010. They aim to present contemporary and historical topics in the theory of isoparametric hypersurfaces and discuss related recently published examples of CR submanifolds of complex projective space. Though we assume little to no background these notes should also hold the interest of an expert. The notion of an n-Sasakian manifold is a generalisation of the notion of a 3-Sasakian manifold. The examples discussed are related to the theory of isoparametric hypersurfaces of spheres with four principal curvatures. These examples carry Einstein metrics and in some special cases carry metrics with positive sectional curvature.

Keywords

  • Riemannian Manifold
  • Covariant Derivative
  • Fundamental Form
  • Curvature Tensor
  • Principal Curvature

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

Thanks go to Daniele Grandini for his reading over drafts, Quo-Shin Chi for his suggestions.

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Correspondence to Owen Dearricott .

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Dearricott, O. (2014). Lectures on n-Sasakian Manifolds. In: Geometry of Manifolds with Non-negative Sectional Curvature. Lecture Notes in Mathematics, vol 2110. Springer, Cham. https://doi.org/10.1007/978-3-319-06373-7_4

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