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  • 제목/요약/키워드: anti-invariant submanifolds

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RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM

  • Kim, Jeong-Sik;Dwivedi, Mohit Kumar;Tripathi, Mukut Mani
    • 대한수학회보
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    • 제46권5호
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    • pp.979-998
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    • 2009
  • Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, θ-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant Θk of different kind of submanifolds of a S-space form ˜M(c) are obtained.

CERTAIN RESULTS ON SUBMANIFOLDS OF GENERALIZED SASAKIAN SPACE-FORMS

  • Yadav, Sunil Kumar;Chaubey, Sudhakar K
    • 호남수학학술지
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    • 제42권1호
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    • pp.123-137
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    • 2020
  • The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.

ON GENERIC SUBMANIFOLDS OF LP-SASAKIAN MANIFOLDS WITH CONCURRENT VECTOR FIELDS

  • Ghosh, Sujoy;Jun, Jae-Bok;Sarkar, Avijit
    • 대한수학회논문집
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    • 제36권2호
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    • pp.361-375
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    • 2021
  • The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D of M are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.

A SHORT NOTE ON BIHARMONIC SUBMANIFOLDS IN 3-DIMENSIONAL GENERALIZED (𝜅, 𝜇)-MANIFOLDS

  • Sasahara, Toru
    • 대한수학회보
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    • 제53권3호
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    • pp.723-732
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    • 2016
  • We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (κ, μ)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (κ, μ)-manifold. Moreover, we determine 3-dimensional generalized (κ, μ)-manifolds which admit a certain kind of proper biharmonic foliation.

NEW RELATIONSHIPS INVOLVING THE MEAN CURVATURE OF SLANT SUBMANIFOLDS IN S-SPACE-FORMS

  • Fernandez, Luis M.;Hans-Uber, Maria Belen
    • 대한수학회지
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    • 제44권3호
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    • pp.647-659
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    • 2007
  • Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.