• 제목/요약/키워드: Product manifolds

검색결과 106건 처리시간 0.022초

CR-WARPED PRODUCT SUBMANIFOLDS OF NEARLY KAEHLER MANIFOLDS

  • Al-Luhaibi, Nadia S.;Al-Solamy, Falleh R.;Khan, Viqar Azam
    • 대한수학회지
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    • 제46권5호
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    • pp.979-995
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    • 2009
  • As warped product manifolds provide an excellent setting to model space time near black holes or bodies with large gravitational field, the study of these manifolds assumes significance in general. B. Y. Chen [4] initiated the study of CR-warped product submanifolds in a Kaehler manifold. He obtained a characterization for a CR-submanifold to be locally a CR-warped product and an estimate for the squared norm of the second fundamental form of CR-warped products in a complex space form (cf [6]). In the present paper, we have obtained a necessary and sufficient conditions in terms of the canonical structures P and F on a CR-submanifold of a nearly Kaehler manifold under which the submanifold reduces to a locally CR-warped product submanifold. Moreover, an estimate for the second fundamental form of the submanifold in a generalized complex space is obtained and thus extend the results of Chen to a more general setting.

SASAKIAN STRUCTURES ON PRODUCTS OF REAL LINE AND KÄHLERIAN MANIFOLD

  • Beldjilali, Gherici;Cherif, Ahmed Mohammed;Zaga, Kaddour
    • Korean Journal of Mathematics
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    • 제27권4호
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    • pp.1061-1075
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    • 2019
  • In this paper, we construct a Sasakian manifold by the product of real line and Kählerian manifold with exact Kähler form. This result demonstrates the close relation between Sasakian and Kählerian manifold with exact Kähler form. We present an example and an open problem.

REMARKS ON METALLIC MAPS BETWEEN METALLIC RIEMANNIAN MANIFOLDS AND CONSTANCY OF CERTAIN MAPS

  • Akyol, Mehmet Akif
    • 호남수학학술지
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    • 제41권2호
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    • pp.343-356
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    • 2019
  • In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain maps between metallic Riemannian manifolds and various manifolds by imposing the holomorphic-like condition. Moreover, we check the reverse case and show that some such maps are constant if there is a condition for this.

DIFFERENTIAL EQUATIONS ON WARPED PRODUCTS

  • JUNG, YOON-TAE;LEE, SANG CHEOL
    • 호남수학학술지
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    • 제28권2호
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    • pp.233-240
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    • 2006
  • In this paper, we consider the problem of achieving a prescribed scalar curvature on warped product manifolds according to fiber manifolds with constant scalar curvature.

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ON THE SPECTRAL GEOMETRY FOR THE JACOBI OPERATORS OF HARMONIC MAPS INTO PRODUCT MANIFOLDS

  • Kang, Tae-Ho;Ki, U-Hang;Pak, Jin-Suk
    • 대한수학회지
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    • 제34권2호
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    • pp.483-500
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    • 1997
  • We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n \times S^n$ or $CP^n \times CP^n$.

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NONCONSTANT WARPING FUNCTIONS ON EINSTEIN LORENTZIAN WARPED PRODUCT MANIFOLDS

  • Jung, Yoon-Tae;Choi, Eun-Hee;Lee, Soo-Young
    • 호남수학학술지
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    • 제40권3호
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    • pp.447-456
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    • 2018
  • In this paper, we consider nonconstant warping functions on Einstein Lorentzian warped product manifolds $M=B{\times}_{f^2}F$ with an 1-dimensional base B which has a negative definite metric. As the results, we discuss that on M the resulting Einstein Lorentzian warped product metric is a future (or past) geodesically complete one outside a compact set.