• Title, Summary, Keyword: associated Riemannian space

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PROJECTIVELY FLAT FINSLER SPACES WITH CERTAIN (α, β)-METRICS

  • Park, Hong-Suh;Park, Ha-Yong;Kim, Byung-Doo;Choi, Eun-Seo
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.649-661
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    • 2003
  • The ($\alpha,\;\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\beta$. In this paper, we discuss the projective flatness of Finsler spaces with certain ($\alpha,\;\beta$)-metrics ([5]) in a locally Minkowski space.

TEICHMÜLLER SPACES OF NONORIENTABLE 3-DIMENSIONAL FLAT MANIFOLDS

  • Kang, Eun Sook;Kim, Ju Young
    • Journal of the Chungcheong Mathematical Society
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    • v.15 no.2
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    • pp.57-66
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    • 2003
  • The various deformation spaces associated with maximal geometric structures on closed oriented 3-manifolds was studied in [2], leaving out the geometry of $\mathbb{R}^3$. In this paper, we study the Weil spaces and Teichm$\ddot{u}$ller spaces of non-orientable 3-dimensional flat Riemannian manifolds. In particular, we find the Teichm$\ddot{u}$ller spaces are homeomorphic to the Euclidean spaces $\mathbb{R}^4$ or $\mathbb{R}^3$ depending on the holonomy group $\mathbb{Z}_2$ or $\mathbb{Z}_2{\times}\mathbb{Z}_2$ respectively.

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GEOMETRY OF ISOPARAMETRIC NULL HYPERSURFACES OF LORENTZIAN MANIFOLDS

  • Ssekajja, Samuel
    • Journal of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.195-213
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    • 2020
  • We define two types of null hypersurfaces as; isoparametric and quasi isoparametric null hypersurfaces of Lorentzian space forms, based on the two shape operators associated with a null hypersurface. We prove that; on any screen conformal isoparametric null hypersurface, the screen geodesics lie on circles in the ambient space. Furthermore, we prove that the screen distributions of isoparametric (or quasi isoparametric) null hypersurfaces with at most two principal curvatures are generally Riemannian products. Several examples are also given to illustrate the main concepts.