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Volumes of certain small geodesic balls and almost-Hermitian geometry

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Abstract

Let D be the characteristic connection of an almost-Hermitian manifold, V mD (r) the volume of a small geodesic ball for the connection D and C C 1D the first non-trivial term of the Taylor expansion of V mD (r). NK-manifolds are characterized in terms of C C 1D and a family of Hermitian manifolds for which ∫ M C C 1D dvol is a spectral invariant is given and one proves that C C 1D and the spectrum of the complex Laplacian, together, determine the class in which a compact Hermitian manifold lines.

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  1. Departamento de Geometria Topologia, Universidad de Valencia, Facultad de Ciencias Matematicas, Burjasot, Valencia, Spain

    V. Miquel

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  1. V. Miquel
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Miquel, V. Volumes of certain small geodesic balls and almost-Hermitian geometry. Geom Dedicata 15, 261–267 (1984). https://doi.org/10.1007/BF00147649

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  • DOI: https://doi.org/10.1007/BF00147649

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