Metric Tensor - Intrinsic Definitions of A Metric

Intrinsic Definitions of A Metric

The notion of a metric can be defined intrinsically using the language of fiber bundles and vector bundles. In these terms, a metric tensor is a function

(5)

from the fiber product of the tangent bundle of M to R such that the restriction of g to each fiber is a nondegenerate bilinear mapping

The mapping (5) is required to be continuous, and often continuously differentiable, smooth, or real analytic, depending on the case of interest, and whether M can support such a structure.

Read more about this topic:  Metric Tensor

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