Results 221 to 230 of about 72,124 (260)

Uniqueness Theorems in Affine Differential Geometry Part II

Results in Mathematics, 1988
[For part I, cf. the review above, Zbl 0646.53008.] The authors investigate equiaffine locally strongly convex surfaces which are equiaffinely complete and have vanishing or negative scalar curvature.
Li, An-Min, Penn, Gabi
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Affine Transformations in Affine Differential Geometry

Results in Mathematics, 1989
For a \(C^{\infty}\) hypersurface immersion f: \(M^ n\to R^{n+1}\), with M orientable, let \(\nabla\) be the affine connection induced by the affine normal and let h be the corresponding (first affine) fundamental form. The author studies the Lie subgroup of those affine transformations of M, with respect to \(\nabla\), that preserve h, namely \(G ...
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Uniqueness Theorems in Affine Differential Geometry Part I

Results in Mathematics, 1988
[For part II, cf. the review below, Zbl 0646.53009).] This is an interesting paper about equiaffine Weingarten surfaces and hypersurfaces continuing investigations of \textit{A. Švec} [Czech. Math. J. 37, 567-572 (1987)], \textit{R. Schneider} [Math. Z. 101, 375-406 (1967; Zbl 0156.201)] and \textit{A. Schwenk} and the reviewer [Arch. Math.
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On completeness in affine differential geometry

Geometriae Dedicata, 1986
The author considers different notions of completeness in affine differential geometry. He gives an example of a spacelike surface M in \({\mathbb{R}}^ 3\), where \({\mathbb{R}}^ 3\) carries the Lorentz-Minkowski- metric, such that the induced metric on M is complete, but the equiaffine metric of M is not complete.
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Some theorems in affine differential geometry

Acta Mathematica Sinica, 1989
This is a very interesting paper presenting topics from affine differential geometry of locally strongly convex hypersurfaces. (1) A locally strongly convex affine hypersphere with zero scalar curvature R of the metric is uniquely determined. Based on this result it was meanwhile possible to finish the classification of all locally strongly convex ...
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Riemann extensions and affine differential geometry

Results in Mathematics, 1988
It was shown by \textit{A. G. Walker} [Convegno Internaz. Geometria Differenz., Venice/Italy 1953, 64-70 (1954; Zbl 0056.154)] that a torsion-free affine connection on a manifold canonically determines a pseudo-Riemannian metric on the cotangent bundle, called the Riemann- extension of the affine connection.
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Equivalence theorems in affine differential geometry

Geometriae Dedicata, 1989
In this paper we establish an affine equivalence theorem for affine submanifolds of the real affine space with arbitrary codimension. Next, this theorem is used to prove the classical congruence theorem for submanifolds of the Euclidean space, and to prove some results on affine hypersurfaces of the real affine space.
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Affine differential geometry of surfaces in ?4

Geometriae Dedicata, 1994
Employing the method of moving frames, i.e. Cartan's algorithm, we find a complete set of invariants for nondegenerate oriented surfacesM2 in ℝ4 relative to the action of the general affine group on ℝ4. The invariants found include a normal bundle, a quadratic form onM2 with values in the normal bundle, a symmetric connection onM2 and a connection on ...
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The Riemannian and Affine Differential Geometry of Product-Spaces

The Annals of Mathematics, 1939
A Riemannian geometry is completely determined by defining over a space a quadratic differential form ds2 = gabdx'dX , called the metric form. Let {PI and {Q} denote two Riemannian spaces, of dimensions p and q, with metric forms whose coefficients are gab and gii . Then the product { P } X { Q } is a welldefined space { R } of dimension r = p + q.
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Affine Differential Geometry of Closed Hypersurfaces^†

Proceedings of the London Mathematical Society, 1967
Hsiung, C., Shahin, J. K.
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