RT Journal Article
T1 Applications of PDEs to the study of affine surface geometry
A1 Gilkey, P.
A1 Valle Regueiro, Xabier
K1 Type A affine surface
K1 Quasi-Einstein equation
K1 Affine Killing vector field
K1 Locally homogeneous affine surface
AB 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.
PB Mathematical Society of Serbia
SN 0025-5165
YR 2019
FD 2019
LK http://hdl.handle.net/10347/21178
UL http://hdl.handle.net/10347/21178
LA eng
NO Gilkey, P. and Valle-Regueiro, X., 2019. Applications of PDEs to the study of affine surface geometry. Matematički Vesnik, 71(1-2), 45-62
NO Supported by projects ED431F 2017/03, and MTM2016-75897-P (Spain)
DS Minerva
RD 23 abr 2026