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with regards to properties of parallel transport of vectors and their length. By demanding that a manifold have an affine parallel transport in such a way that the manifold is locally an
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Additionally, he claimed that the manifold must have a particular parallel transport in which the ratio of two transported vectors is fixed. The corresponding connection
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a metric space. In this sense, Weyl was not just referring to one metric but to the conformal structure defined by
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488:) are examples of recurrent tensors that find importance in mathematical research. For example, if
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is called a Weyl structure, which more generally is defined as a map with property
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1340:{\displaystyle \nabla {\mathcal {R}}=\omega \otimes {\mathcal {R}}}
588:. Historically, Weyl structures emerged from the considerations of
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Recurrent
Tensors on a Linearly Connected Differentiable Manifold
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is a parallel and therefore recurrent tensor with respect to its
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1417:, The Quarterly Journal of Mathematics 1949, Oxford Univ. Press
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One more example of a recurrent tensor is the curvature tensor
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996:{\displaystyle \varphi \rightarrow \varphi -d\lambda }
792:. Such a metric is a recurrent tensor with respect to
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1145:{\displaystyle F(e^{\lambda }g):=\varphi -d\lambda }
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may be too technical for most readers to understand
1423:On symmetric recurrent tensors of the second order
1414:On parallel fields of partially null vector spaces
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1454:Recent developments in pseudo-Riemannian geometry
1403:Weyl, H. (1918). "Gravitation und Elektrizität".
1261:{\displaystyle F(e^{\lambda }g)=F(g)-d\lambda }
1050:{\displaystyle F:\rightarrow \Lambda ^{1}(M)}
8:
286:{\displaystyle \nabla T=\omega \otimes T.\,}
1405:Sitzungsberichte der Preuss. Akad. D. Wiss.
762:{\displaystyle \nabla 'g=\varphi \otimes g}
584:Another example appears in connection with
310:are parallel tensors which are defined by
57:Learn how and when to remove these messages
941:{\displaystyle g\rightarrow e^{\lambda }g}
508:is a recurrent non-null vector field on a
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107:Learn how and when to remove this message
91:, without removing the technical details.
1444:, Journal of Differential Geometry 1970
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456:and its property to be torsion-free.
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1456:. European Mathematical Society.
38:This article has multiple issues.
345:with respect to some connection
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1003:. This induces a canonical map
446:{\displaystyle \nabla ^{LC}g=0}
46:or discuss these issues on the
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335:{\displaystyle \nabla A=0}
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306:An example for recurrent
1363:Alekseevsky, Baum (2008)
961:{\displaystyle \varphi }
810:{\displaystyle \nabla '}
785:{\displaystyle \varphi }
719:{\displaystyle \nabla '}
459:Parallel vector fields (
862:{\displaystyle \nabla }
849:with affine connection
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219:{\displaystyle \nabla }
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1195:{\displaystyle F}
902:{\displaystyle g}
882:{\displaystyle g}
501:{\displaystyle X}
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594:affine space
590:Hermann Weyl
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580:Metric space
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97:October 2021
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40:Please help
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1372:Weyl (1918)
1095:defined by
948:, the form
512:satisfying
193:mathematics
1475:Categories
1397:Literature
1352:References
251:such that
205:connection
153:; try the
140:link to it
43:improve it
1328:⊗
1325:ω
1312:∇
1256:λ
1250:−
1224:λ
1140:λ
1134:−
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1117:λ
1030:Λ
1026:→
991:λ
985:−
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976:φ
956:φ
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923:→
857:∇
801:∇
780:φ
754:⊗
751:φ
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467:∇
423:∇
353:∇
321:∇
274:⊗
271:ω
262:∇
214:∇
162:July 2021
143:. Please
49:talk page
1452:(2008).
804:′
741:′
713:′
555:one-form
297:Examples
242:one-form
228:manifold
1486:Tensors
1450:H. Baum
308:tensors
233:, is a
197:physics
83:Please
1460:
1407:: 465.
1156:where
235:tensor
136:orphan
134:is an
226:on a
1458:ISBN
199:, a
195:and
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247:on
191:In
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