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A NONLINEAR PARTIAL DIFFERENTIAL EQUATION RELATED WITH CERTAIN SPACES WITH GENERAL CONNECTIONS(II)

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SUT Journal of Mathematics Vol. 32, No. 1 (1996), 1–33

A NONLINEAR PARTIAL DIFFERENTIAL

EQUATION RELATED WITH CERTAIN SPACES

WITH GENERAL CONNECTIONS(II)

Tominosuke OTSUKI

(Received May 9, 1995)

Abstract. From a Minkowski-type metric on Rn+ satisfying the Einstein

con-dition, we derive a nonlinear partial differential equation. In order to know the property of its solutions, we obtain an approximate solution with certain boundary conditions numerically by the finite element method, which will give us some clues to get theoretical solutions.

AMS 1991 Mathematics Subject Classification. Primary 53C05, 53C22. Key words and phrases. General Connections, Minkowski Type, Einstein

Con-dition.

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NONLINEAR PARTIAL DIFFERENTIAL EQUATION (II) 33

Tominosuke OTSUKI

Department of Mathematics, Science University of Tokyo Wakamiya-cho 26, Shinjuku-ku, Tokyo 162, JAPAN

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