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November 2006 The variational formulas of the volume function in the equiaffine geometry
Naoyuki KOIKE
Hokkaido Math. J. 35(4): 719-751 (November 2006). DOI: 10.14492/hokmj/1285766427

Abstract

We obtain the first and second variational formulas for the volume function over the space of all equiaffine immersions. By using the first variational formula, we define some kinds of volume functions over the space of all non-degenerate immersions and obtain the Euler-Lagrange equation for those volume functions. Also, in the case where the ambient space is flat, we obtain the second variational formulas for special ones of those volume functions.

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Naoyuki KOIKE. "The variational formulas of the volume function in the equiaffine geometry." Hokkaido Math. J. 35 (4) 719 - 751, November 2006. https://doi.org/10.14492/hokmj/1285766427

Information

Published: November 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1122.53007
MathSciNet: MR2289358
Digital Object Identifier: 10.14492/hokmj/1285766427

Subjects:
Primary: 53A15

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 4 • November 2006
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