NONHOLONOMIC ALGEBROIDS, FINSLER GEOMETRY, AND LAGRANGE-HAMILTON SPACES

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VACARU SERGIU I.

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-33

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Title

NONHOLONOMIC ALGEBROIDS, FINSLER GEOMETRY, AND LAGRANGE-HAMILTON SPACES

Author(s)

VACARU SERGIU I. | Issue Writer Certificate

Keywords

LIE ALGEBROIDS

LAGRANGE

HAMILTON AND RIEMANN-FINSLER SPACES

NONLINEAR CONNECTION

NONHOLONOMIC MANIFOLD

GEOMETRIC MECHANICS AND GRAVITY THEORIES

Abstract

We elaborate a unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on LIE ALGEBROIDS provided with NONLINEAR CONNECTION (N-connection) structure. There are investigated conditions when the fundamental geometric objects (anchor, metric and linear connection, almost symplectic, and related almost complex structures) may be canonically defined by an N-connection induced from a regular Lagrangian (or Hamiltonian), in mechanical models, or by generic off-diagonal metric terms and nonholonomic frames, in gravity theories. Such geometric constructions are modelled on NONHOLONOMIC MANIFOLDs provided with nonintegrable distributions and related chains of exact sequences of submanifolds defining N-connections. We investigate the main properties of the LAGRANGE, Hamilton, Finsler-Riemann and Einstein-Cartan algebroids, construct and analyze exact solutions describing such objects.

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APA: Copy

VACARU, SERGIU I.. (2012). NONHOLONOMIC ALGEBROIDS, FINSLER GEOMETRY, AND LAGRANGE-HAMILTON SPACES. MATHEMATICAL SCIENCES, 6(-), 1-33. SID. https://sid.ir/paper/322585/en

Vancouver: Copy

VACARU SERGIU I.. NONHOLONOMIC ALGEBROIDS, FINSLER GEOMETRY, AND LAGRANGE-HAMILTON SPACES. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-33. Available from: https://sid.ir/paper/322585/en

IEEE: Copy

SERGIU I. VACARU, “NONHOLONOMIC ALGEBROIDS, FINSLER GEOMETRY, AND LAGRANGE-HAMILTON SPACES,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–33, 2012, [Online]. Available: https://sid.ir/paper/322585/en

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