논문KCI 등재
Scalar curvature of contact three CR-submanifolds in a unit (4m+3)-sphere
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초록
In this paper we derive an integral formula on an (n+3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere S^(4m+3). Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.
Abstract
In this paper we derive an integral formula on an (n+3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere S^(4m+3). Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.
참고문헌 (10)
- A. Bejancu, "Geometry of CR-submanifolds" (1986), D. Reidel Publishing Company
- B. Y. Chen, "Geometry of Submanifolds" (1973), Marcel Dekker Inc
- J. Erbacher, "Reduction of the codimension of an isometric immersion", J. Diff. Geom, 5, pp.333~340 (1971)
- S. Ishihara, "Differential geometry of fibred spaces" (1973), Study Group of Dif- ferential Geometry
- T. Kashiwada, "A note on a Riemannian space with Sasakian 3-structure", Natur. Sci. Rep. Ochanomizu Univ, 22, pp.1~2 (1971)
- Y. Y. Kuo, "On almost contact 3-structure", Tohoku Math. J, 22, pp.325~332 (1970)
- J.-H. Kwon, "On contact three CR-submanifolds of a (4m+3)-dimensional unit sphere", Comm. Korean Math Soc, 13(3), pp.561~577 (1998)
- J. S. Pak, "Real hypersurfaces in quaternionic Kaehlerian manifolds with constant Q- sectional curvature", Kodai Math. Sem. Rep, 29(1), pp.22~61 (1977)
- K. Yano, "Integral formulas in Riemannian geometry" (1970), Marcel Dekker Inc
- K. Yano, "CR submanifolds of Kaehlerian and Sasakian manifolds" (1983), Birkhauser
관련 논문AI추천
SCALAR CURVATURE OF CONTACT CR-SUBMANIFOLDS IN AN ODD-DIMENSIONAL UNIT SPHERE김향숙, 박진석대한수학회 · 대한수학회보2010 · 제47권 제3호Certain class of contact CR-submanifolds of a Sasakian space form김향숙, 박진석, Don Kwon Choi대한수학회 · 대한수학회논문집2014 · 제29권 제1호Contact three $CR$-submanifolds of a $(4m+3)$-dimensional unit sphere권정환, 김영미, 김향숙, 박진석대한수학회 · 대한수학회지2007 · 제44권 제2호Submanifolds of Codimension 3 in a Complex Space Form with Commuting Structure Jacobi Operator기우항, 송현정경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제1호Existence of Proper Contact CR Product and Mixed Foliate Contact CR Submanifolds of E^{2m+1} (-3)김향숙, 박은미, 박진숙영남수학회 · East Asian Mathematical Journal2014 · 제30권 제1호CODIMENSION REDUCTION FOR SUBMANIFOLDS OF UNIT (4m+ 3)-SPHERE AND ITS APPLICATIONS김향숙, 박진석대한수학회 · 대한수학회보2014 · 제51권 제5호
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