On the Ricci curvature tensor of \((k+1)\)-dimensional semi-ruled surfaces in \(E_\nu^{n+1}\) (Q1591093)
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scientific article; zbMATH DE number 1545878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Ricci curvature tensor of \((k+1)\)-dimensional semi-ruled surfaces in \(E_\nu^{n+1}\) |
scientific article; zbMATH DE number 1545878 |
Statements
On the Ricci curvature tensor of \((k+1)\)-dimensional semi-ruled surfaces in \(E_\nu^{n+1}\) (English)
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8 April 2002
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Given a curve \(\alpha(t)=(\alpha_1(t),\dots,\alpha_{n+t}(t))\) in an \((n+1)\)-dimensional semi-Euclidean space \(E\). Let \(E_{k,\mu}\) be a \(k\)-dimensional subspace of \(E\), generated by \(\{e_1(t),\dots,e_k(t)\}\), where \(\mu\) is its index. As \(E_{k,\mu}\) moves along a curve \(\alpha\) in \(E\), it forms a \((k+1)\)-dimensional surface \(S\), called a generalized semi-ruled surface in \(E\). In this paper, the authors find a local expression for the Ricci tensor of \(S\).
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semi-Euclidean space
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generalized semi-ruled surface
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Ricci tensor
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0.9242303371429444
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