The variational formulas of the volume function in the equiaffine geometry (Q2372690)
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| Language | Label | Description | Also known as |
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| English | The variational formulas of the volume function in the equiaffine geometry |
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The variational formulas of the volume function in the equiaffine geometry (English)
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1 August 2007
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In this paper, the first and second variational formulas for the volume function over the space of all equiaffine immersions are given. Then, using the first variational formula, some kinds of volume functions over the space of all non degenerate immersions are defined and the Euler-Lagrange equations for those volume functions are obtained. Also some special cases, for example, flat ambient space, c-Blaschke immersion, are considered.
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equiaffine immersion
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variational formula
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Tchebychev tensor field
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volume ratio function
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