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A Differential Relation of Metric Properties for Orientable Smooth Surfaces in ℝ 3

Author

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  • Sungmin Ryu

    (Department of Mechanical Engineering, Incheon National University, Academy-ro 119, Incheon 22012, Republic of Korea)

Abstract

The Gauss–Bonnet formula finds applications in various fundamental fields. Global or local analysis on the basis of this formula is possible only in integral form since the Gauss–Bonnet formula depends on the choice of a simple region of an orientable smooth surface S . The objective of the present paper is to construct a differential relation of the metric properties concerned at a point on S . Pointwise analysis on S is possible through the differential relation, which is expected to provide new geometrical insights into existing studies where the Gauss–Bonnet formula is applied in integral form.

Suggested Citation

  • Sungmin Ryu, 2023. "A Differential Relation of Metric Properties for Orientable Smooth Surfaces in ℝ 3," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2337-:d:1148988
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    Cited by:

    1. Sungmin Ryu, 2023. "Physics-to-Geometry Transformation to Construct Identities between Reynolds Stresses," Mathematics, MDPI, vol. 11(17), pages 1-10, August.

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