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The Riemann tensor for nonholonomic manifolds
"... Abstract. For every nonholonomic manifold, i.e., manifold with nonintegrable distribution the analog of the Riemann tensor is introduced. It is calculated here for the contact and Engel structures: for the contact structure it vanishes (another proof of Darboux’s canonical form); for the Engel distr ..."
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Cited by 11 (5 self)
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Abstract. For every nonholonomic manifold, i.e., manifold with nonintegrable distribution the analog of the Riemann tensor is introduced. It is calculated here for the contact and Engel structures: for the contact structure it vanishes (another proof of Darboux’s canonical form); for the Engel
Intuitive Curvature: No Relation to the Riemann Tensor
"... MerriamWebster’s Collegiate Dictionary, Eleventh Edition, gives a technical definition of curvature, “the rate of change of the angle through which the tangent to a curve turns in moving along the curve and which for a circle is equal to the reciprocal of the radius”. That precisely describes a cur ..."
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curve’s intuitive curvature, but the Riemann “curvature ” tensor is zero for all curves! We work out the natural extension of intuitive curvature to hypersurfaces, based on the rates that their tangents develop components which are orthogonal to the local tangent hyperplane. Intuitive curvature is seen
of the Riemann tensor and the KalbRamond H
, 2003
"... The twoloop effective action and some symmetries ..."
SECOND ORDER SCALAR INVARIANTS OF THE RIEMANN TENSOR:
, 2003
"... We discuss the Kretschmann, ChernPontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the NewmanPenrose formalism and in the framework of gravitoelectromagnetism, using the KerrNewman geometry as an example. An analogy with electromagn ..."
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We discuss the Kretschmann, ChernPontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the NewmanPenrose formalism and in the framework of gravitoelectromagnetism, using the KerrNewman geometry as an example. An analogy
THE ANALOGS OF THE RIEMANN TENSOR FOR EXCEPTIONAL STRUCTURES ON SUPERMANIFOLDS
, 2005
"... H. Hertz called any manifold M with a given nonintegrable distribution nonholonomic. Vershik and Gershkovich stated and R. Montgomery proved that the space of germs of any nonholonomic distribution on M with an open and dense orbit of the diffeomorphism group is either (1) of codimension one or (2 ..."
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series similar to contact ones and 11 exceptional algebras preserving nonholonomic structures. Here we compute the cohomology corresponding to the analog of the Riemann tensor for the supermanifolds corresponding to the 15 exceptional simple vectorial Lie superalgebras, 11 of which are nonholonomic
A SECONDORDER IDENTITY FOR THE RIEMANN TENSOR AND APPLICATIONS
, 2011
"... A secondorder differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed. ..."
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A secondorder differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed
Results 1  10
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426