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The differential geometry of fracture [PDF]
Acta Mechanica, 1978 The methods of differential geometry have been applied to the process of cracking. In particular, it is shown that a crack may be viewed as an imperfectly torn elastically distorted space. Such a space in turn is characterized by the presence of a quantity termed an anholonomic object.
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The differential geometry of webs [PDF]
Journal of Soviet Mathematics, 1985 This survey paper is a continuation of the survey paper by \textit{V. D. Belousov} and \textit{V. V. Ryzhkov} [Itogi Nauki Tekh., Ser. Algebra Topol. Geom. 10, 159--188 (1972; Zbl 0275.53005)] and its aim is to present results obtained especially in the Soviet Union in the last years in the geometry of webs.
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The differential geometry of bending
Meccanica, 1978The deformation associated with uniform bending has been treated using the techniques of differential geometry. The Burgers circuit as well as various related tensor quantities such as torsion and dislocation density have all been determinated with respect to these various states of deformation.
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On the Differential Geometry of Foliations
The Annals of Mathematics, 1960This paper has its roots in the well-known work of Reeb and its recent generalization by Reinhart [9], [10], as well as in much older, incomplete work of E. Cartan dealing with the differential-geometric structure of a foliation [3]. The general problem is to see how the structure affects the global properties of the foliation.
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Notes on Differential Geometry
The Annals of Mathematics, 19311. By an oval we mean a convex closed curve. For the sake of simplicity the following discussion will be restricted to curves whose curvature is continuous and never vanishes, although our results can be extended, with suitable modifications, to the general case.
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Stochastic differential geometry
Russian Mathematical Surveys, 1983The paper gives another exposition of what is now called ''Malliavin's stochastic calculus''. The approach is somewhat close to the Bismut's one. The results are extended to the case of diffusion processes on infinite dimensional smooth manifolds. This enables the author to construct certain quasi-invariant measures on infinite dimensional Lie groups ...
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Differential geometry of strips
Journal of Soviet Mathematics, 1980A survey of papers on the geometry of multidimensional strip surfaces and their generalizations.
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2007
The main objective of this chapter is to present a Clifford bundle formalism for the formulation of the differential geometry of a manifold M, equipped with metric fields \(\boldsymbol{g} \in \sec T_{2}^{0}M\) and \(\mathtt{g} \in \sec T_{0}^{2}M\) for the tangent and cotangent bundles.
Waldyr A. Rodrigues +1 more
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The main objective of this chapter is to present a Clifford bundle formalism for the formulation of the differential geometry of a manifold M, equipped with metric fields \(\boldsymbol{g} \in \sec T_{2}^{0}M\) and \(\mathtt{g} \in \sec T_{0}^{2}M\) for the tangent and cotangent bundles.
Waldyr A. Rodrigues +1 more
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geometry of differential equations
Journal of Soviet Mathematics, 1983This paper contains a survey of papers on the geometry of differential equations, which appeared no earlier than 1972, continuing the general survey (RZhMat, 1974, 11A800), and considers in more detail a special cycle of investigations of the geometry of systems of partial differential equations, distinguished by the presence of practical applications.
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