What question did this study set out to answer?

This research aims to explore the properties of locally definable C^γG manifolds in relation to C^sG manifolds.

June 3, 2026Open Access

局所デファイナブルCʳG多様体の局所デファイナブルCˢG多様体構造について

Key Points

This research aims to explore the properties of locally definable C^γG manifolds in relation to C^sG manifolds.
Defined locally definable C^γG manifolds and examined their properties in relation to affine structures.
Demonstrated that each affine locally definable C^γG manifold is diffeomorphic to a locally definable C^sG manifold.
Established conditions for C^1G diffeomorphism between two affine locally definable C^γG manifolds.
Every affine locally definable C^γG manifold can be locally defined as C^sG.
Two affine locally definable C^γG manifolds are C^1G diffeomorphic if they are locally definable as C^γG.

Abstract

Let G be a finite group. We define locally definable C^γG (1≤γ≤ω) manifolds as generalizations of definable C^γG manifolds (1≤γ≤ω). Let 0<γ<s<∞. We prove that every affine locally definable C^γG manifold is locally definably C^γG diffeomorphic to a locally definable CSG manifold. Moreover we prove that for any two affine locally definable C^γG manifolds, they are C¹G diffeomorphic if and only if they are locally definable C^γG diffeomorphic.

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Cite This Study

Tomohiro KAWAKAMI (Tue,) studied this question.

synapsesocial.com/papers/6a1fc4bbdee9eb8c0dce62e8 https://doi.org/https://doi.org/10.19002/an00257977.56.1

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