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Extension to Arbitrary Tensors

In: Introduction to Tensor Analysis and the Calculus of Moving Surfaces

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  • Pavel Grinfeld

    (Drexel University, Department of Mathematics)

Abstract

In Chap. 15, the invariant derivative operator $$\dot{\nabla }$$ was defined for variants of order zero. The new operator proved to have a number of essential features including the tensor property—that is, producing tensor outputs for tensor inputs. Even with that narrow definition, the new operator demonstrated its impressive utility in equations (15.54) and (15.56) for evaluating the rates of change of volume and surface integrals. However, analysis of all but a few problems is impossible, unless the new derivative is extended to all objects encountered on surfaces which includes variants with arbitrary indicial signatures. The development of this extension is the subject of this chapter.

Suggested Citation

  • Pavel Grinfeld, 2013. "Extension to Arbitrary Tensors," Springer Books, in: Introduction to Tensor Analysis and the Calculus of Moving Surfaces, edition 127, chapter 0, pages 267-277, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7867-6_16
    DOI: 10.1007/978-1-4614-7867-6_16
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