Applications of PDEs to the study of affine surface geometry
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Título: | Applications of PDEs to the study of affine surface geometry |
Autor/a: | Gilkey, P. Valle Regueiro, Xabier |
Centro/Departamento: | Universidade de Santiago de Compostela. Departamento de Matemáticas |
Palabras chave: | Type A affine surface | Quasi-Einstein equation | Affine Killing vector field | Locally homogeneous affine surface | |
Data: | 2019 |
Editor: | Mathematical Society of Serbia |
Cita bibliográfica: | Gilkey, P. and Valle-Regueiro, X., 2019. Applications of PDEs to the study of affine surface geometry. Matematički Vesnik, 71(1-2), 45-62 |
Resumo: | If M=(M,∇) is an affine surface, let Q(M):=ker(H+1m−1ρs) be the space of solutions to the quasi-Einstein equation for the crucial eigenvalue. Let M~=(M,∇~) be another affine structure on M which is strongly projectively flat. We show that Q(M)=Q(M~) if and only if ∇=∇~ and that Q(M) is linearly equivalent to Q(M~) if and only if M is linearly equivalent to M~. We use these observations to classify the flat Type A connections up to linear equivalence, to classify the Type A connections where the Ricci tensor has rank 1 up to linear equivalence, and to study the moduli spaces of Type A connections where the Ricci tensor is non-degenerate up to affine equivalence. |
Versión do editor: | http://www.vesnik.math.rs/vol/mv191205.pdf |
URI: | http://hdl.handle.net/10347/21178 |
ISSN: | 0025-5165 |
E-ISSN: | 2406-0682 |
Dereitos: | © 2019 by de authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) lisense (https://creativecommons.org/licenses/by/4.0/) |
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