Search results for "Fundamental theorem of Riemannian geometry"

showing 4 items of 4 documents

Linear invariants of Riemannian almost product manifolds

1982

Using the decomposition of a certain vector space under the action of the structure group of Riemannian almost product manifolds, A. M. Naveira (9) has found thirty-six distinguished classes of these manifolds. In this article, we prove that this decomposition is irreducible by computing a basis of the space of invariant quadratic forms on such a space.

Discrete mathematicsPure mathematicsCurvature of Riemannian manifoldsGeneral MathematicsLinear invariantsFundamental theorem of Riemannian geometryRiemannian geometryManifoldsymbols.namesakeRicci-flat manifoldProduct (mathematics)symbolsDifferential topologyMathematics::Differential GeometryMathematicsMathematical Proceedings of the Cambridge Philosophical Society
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Some remarks on minimal surfaces in riemannian manifolds

1970

Pure mathematicsCurvature of Riemannian manifoldsRiemannian submersionApplied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisFundamental theorem of Riemannian geometryRiemannian geometry01 natural sciencesLevi-Civita connectionsymbols.namesakeRicci-flat manifold0103 physical sciencessymbolsMinimal volume010307 mathematical physicsSectional curvature0101 mathematicsMathematicsCommunications on Pure and Applied Mathematics
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Feuilletages Riemanniens singuliers

2006

Abstract We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

Pure mathematicsMathematical analysisGeneral MedicineRiemannian geometryFundamental theorem of Riemannian geometryPseudo-Riemannian manifoldLevi-Civita connectionsymbols.namesakesymbolsMinimal volumeMathematics::Differential GeometryExponential map (Riemannian geometry)Ricci curvatureScalar curvatureMathematicsComptes Rendus Mathematique
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Geodesic flow of the averaged controlled Kepler equation

2008

A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyGeodesicGeneral MathematicsCut locusConformal map02 engineering and technologyKepler's equationFundamental theorem of Riemannian geometry01 natural sciencesConvexityIntrinsic metricsymbols.namesake020901 industrial engineering & automationSingularity0101 mathematicsorbit transferMathematicsApplied Mathematics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]cut and conjugate lociRiemannian metrics49K15 70Q05symbols[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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