Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022

Daniele Angella [a] and Francesco Pediconi [a]

A survey on locally homogeneous almost-Hermitian spaces

Pages: 373-418
Received: 29 November 2021
Accepted: 27 September 2022
Mathematics Subject Classification: 53C30, 53C55, 53E30.
Keywords: Locally homogeneous space, almost-Hermitian, Gauduchon connections.
Authors address:
[a]: Università degli Studi di Firenze, Dipartimento di Matematica e Informatica ''Ulisse Dini'', Firenze, Italy

The authors are supported by project PRIN2017 ''Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics'' (code 2017JZ2SW5), and by GNSAGA of INdAM

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Abstract: We survey the theory of locally homogeneous almost-Hermitian spaces. In particular, by using the framework of varying Lie brackets, we write formulas for the curvature of all the Gauduchon connections and we provide explicit examples of computations.

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