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Extended tensorial curvature analysis for embeddings and foliations. (English) Zbl 0877.57013
Nencka, Hanna (ed.) et al., Geometry and nature: in memory of W. K. Clifford. A conference on new trends in geometrical and topological methods, July 30–August 5, 1995, Madeira, Portugal. Providence, RI: American Mathematical Society. Contemp. Math. 203, 207-219 (1997).
The author summarizes the techniques and methods in the evolution of differential geometry and new physical problems: the first deformation tensor and the second fundamental tensor, the rotation tensor, adapted foliation connection etc. The main results of the work show how the classical tensor formalism attached to an embedded p-surface provides a concise and flexible machinery for the generalized curvature analysis of embedded p-surfaces and foliations necessary in cosmology and physics.
MSC:
57R30Foliations; geometric theory (differential topology)
53B21Methods of Riemannian geometry
70G45Differential-geometric methods for dynamical systems