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This paintings is meant to offer the scholar a attached account of the topic of the differential invariants of generalized areas, together with the attention-grabbing and demanding discoveries within the box by way of Levi-Civita, Weyl, and the writer himself, and theories of Schouten, Veblen, Eisenhart and others.

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Elworthy to interpret this last term as a stochastic integral. This leads to rather complicated analysis but he was able to develop a de Rham theory, [L´ea96]. Much earlier there had been an approach by Jones and L´eandre using stochastic Chen forms, [JL91]. However Hodge–Kodaira theory, and a more standard form of L 2 -cohomology did not appear in this work. A different approach, by Elworthy and Li, was to modify the space of H-forms. This was done by using the conditional expectation m r ∧r T Iσ : ∧r L 2,1 0 ([0, T ] : R ) → ∧ Tσ C x0 of ∧r T I, ‘ﬁltering out the redundant noise’ or ‘integrating over the ﬁbres of I,’ [EL00].

58(7):923–940, 2005. A Lie Group Structure for Automorphisms of a Contact Weyl Manifold Naoya Miyazaki∗ Department of Mathematics, Faculty of Economics, Keio University, Yokohama, 223-8521, Japan. jp Dedicated to Professor Hideki Omori Summary. In the present article, we are concerned with the automorphisms of a contact Weyl manifold, and we introduce an inﬁnite-dimensional Lie group structure for the automorphism group. AMS Subject Classiﬁcation: Primary 58B25; Secondary 53D55 Key words: Inﬁnite-dimensional Lie group, contact Weyl manifold, star product, deformation quantization.

Philos. Trans. Roy. Soc. London Ser. A, 308(1505):523–615, 1983. S. Aida and B. K. Driver. Equivalence of heat kernel measure and pinned Wiener measure on loop groups. R. Acad. Sci. Paris S´er. , 331(9):709–712, 2000. S. Albeverio, A. Daletskii, and Y. Kondratiev. De Rham complex over product manifolds: Dirichlet forms and stochastic dynamics. In Mathematical physics and stochastic analysis (Lisbon, 1998), pages 37–53. World Sci. Publishing, River Edge, NJ, 2000. S. Aida. Stochastic analysis on loop spaces [translation of S¯ugaku 50 (1998), no.