منابع مشابه
Affine Connections, and Midpoint Formation
It is a striking fact that differential calculus exists not only in analysis (based on the real numbers R), but also in algebraic geometry, where no limit processes are available. In algebraic geometry, one rather uses the idea of nilpotent elements in the “affine line” R; they act as infinitesimals. (Recall that an element x in a ring R is called nilpotent if xk = 0 for suitable non-negative i...
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If ∇ is a torsionless connection on the tangent bundle of a manifold M the Weyl curvature W is the part of the curvature in kernel of the Ricci contraction. We give a coordinate free proof of Weyl’s result that W vanishes if and only if (M,∇) is (locally) diffeomorphic to RP with ∇, when transported to RP, in the projective class of ∇LC , the Levi-Civita connection of the Fubini–Study metric on...
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The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
متن کاملAffine connections, midpoint formation, and point reflection
It is a striking fact that differential calculus exists not only in analysis (based on the real numbers R and limits therein), but also in algebraic geometry, where no limit processes are available. In algebraic geometry, one rather uses the idea of nilpotent elements in the “affine line” R; they act as infinitesimals. (Recall that an element x in a ring R is called nilpotent if xk = 0 for suit...
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ژورنال
عنوان ژورنال: Mediterranean Journal of Mathematics
سال: 2015
ISSN: 1660-5446,1660-5454
DOI: 10.1007/s00009-015-0559-6