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Self-similar Hessian and conformally Kähler manifolds

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Abstract

A self-similar Hessian (special Kähler) manifold is a Hessian (special Kähler) manifold \((M,\nabla ,g)\) endowed with an affine (holomorphic) homothetic vector field \(\xi \). Consider an action of a group G on a self-similar Hessian (special Kähler) manifold \((M,\nabla ,g,\xi )\) by affine (holomorphic) isometries preserving \(\xi \) such that G acts on the level set \(\{g(\xi ,\xi )=1\}\) simply transitively. Then, we construct a homogeneous conformally Kähler (hyper Kähler) structure on TM \((T^*M)\).

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  1. Department of Mathematics, Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Russian Federation, Moscow, Russia

    Pavel Osipov

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  1. Pavel Osipov
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Correspondence to Pavel Osipov.

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The article was prepared within the framework of the HSE University Basic Research Program and the contest “Young Russian Mathematics”.

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Osipov, P. Self-similar Hessian and conformally Kähler manifolds. Ann Glob Anal Geom 62, 479–488 (2022). https://doi.org/10.1007/s10455-022-09861-1

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