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2001•East Asian Mathematical JournalRequires access

ON A HYPERSURFACE OF THE FIRST APPROXIMATE MATSUMOTO SPACE

Il‐Yong Lee, Dong-Gum Jun

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Abstract

We consider the special hypersurface of the first approximate Matsumoto metric with being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

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What this paper is about

We consider the special hypersurface of the first approximate Matsumoto metric with being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

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Available abstract

We consider the special hypersurface of the first approximate Matsumoto metric with being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

Key concepts: Hypersurface, Hyperplane, Mathematics, Mathematical analysis, Constant (computer programming), Plane (geometry), Metric (unit), Scalar (mathematics)

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