The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Peter B. Gilkey - One of the best experts on this subject based on the ideXlab platform.
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Geometric Realizations of Para-Hermitian Curvature Models
Results in Mathematics, 2009Co-Authors: Miguel Brozos-vázquez, Stana Nikcevic, Peter B. Gilkey, Ramón Vázquez-lorenzoAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri–Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
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Geometric Realizations of Hermitian curvature models
arXiv: Differential Geometry, 2008Co-Authors: Miguel Brozos-vázquez, Peter B. Gilkey, H. Kang, Stana NikcevicAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
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relating the curvature tensor and the complex jacobi operator of an almost Hermitian Manifold
Advances in Geometry, 2008Co-Authors: M Brozosvazquez, Eduardo Garciario, Peter B. GilkeyAbstract:Let J be a unitary almost complex structure on a Riemannian Manifold (M, g). If x is a unit tangent vector, let π := Span{x, Jx} be the associated complex line in the tangent bundle of M . The complex Jacobi operator and the complex curvature operators are defined, respectively, by J (π) := J (x) + J (Jx) and R(π) := R(x, Jx). We show that if (M, g) is Hermitian or if (M,g) is nearly Kahler, then either the complex Jacobi operator or the complex curvature operator completely determine the full curvature operator; this generalizes a well known result in the real setting to the complex setting. We also show this result fails for general almost Hermitian Manifolds.
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relating the curvature tensor and the complex jacobi operator of an almost Hermitian Manifold
arXiv: Differential Geometry, 2006Co-Authors: M Brozosvazquez, Eduardo Garciario, Peter B. GilkeyAbstract:Let J be a unitary almost complex structure on a Riemannian Manifold (M,g). If x is a unit tangent vector, let P be the associated complex line spanned by x and by Jx. We show that if (M,g) is Hermitian or if (M,g) is nearly Kaehler, then either the complex Jacobi operator (JC(P)y=R(y,x)x+R(y,Jx)Jx) or the complex curvature operator (RC(P)y=R(x,Jx)y) completely determine the full curvature operator; this generalizes a well known result in the real setting to the complex setting. We also show this result fails for general almost Hermitian Manifold.
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the local index formula for a Hermitian Manifold
Pacific Journal of Mathematics, 1997Co-Authors: Peter B. Gilkey, Stana Nikcevic, J PohjanpeltoAbstract:Let M be a compact complex Manifold of real dimension m = 2m with a Hermitian metric. Let an(x,∆) be the heat equation asymptotics of the complex Laplacian ∆. Then TrL2(fe−t∆ p,q ) ∼ Σn=0t ∫ M fan(x,∆) for any f ∈ C∞(M); the an vanish for n odd. Let ag(M) be the arithmetic genus and let an(x, ∂) := Σq(−1)an(x,∆) be the supertrace of the heat equation asymptotics. Then ∫ M an(x, ∂)dx = 0 if n 6= m while ∫ M am(x, ∂)dx = ag(M). The Todd polynomial Tdm is the integrand of the Riemann Roch Hirzebruch formula. If the metric on M is Kaehler, then the local index theorem holds:
Ramón Vázquez-lorenzo - One of the best experts on this subject based on the ideXlab platform.
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Geometric Realizations of Para-Hermitian Curvature Models
Results in Mathematics, 2009Co-Authors: Miguel Brozos-vázquez, Stana Nikcevic, Peter B. Gilkey, Ramón Vázquez-lorenzoAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri–Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
B B Chaturvedi - One of the best experts on this subject based on the ideXlab platform.
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On Ricci pseudo-symmetric super quasi-Einstein Hermitian Manifolds
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2020Co-Authors: B K Gupta, B B ChaturvediAbstract:The present paper deals the study of a Bochner Ricci pseudosymmetric super quasi-Einstein Hermitian Manifold and a holomorphically projective Ricci pseudo-symmetric super quasi-Einstein Hermitian Manifold.
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on bochner ricci semi symmetric Hermitian Manifold
Acta Mathematica Universitatis Comenianae, 2017Co-Authors: B K Gupta, B B ChaturvediAbstract:The aim of the present paper is to study Bochner Ricci semi-symmetric quasi-Einstein Hermitian Manifold (QEH)n, Bochner Ricci semi-symmetric generalised quasi-Einstein Hermitain Manifold G(QEH)n and Bochner Ricci semisymmetric pseudo generalised quasi-Einstein Hermitian Manifold P(GQEH)n.
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conformal transformation in an almost Hermitian Manifold
Novi Sad Journal of Mathematics, 2016Co-Authors: B B Chaturvedi, Pankaj PandeyAbstract:In this paper, we have studied a conformal transformation between two almost Hermitian Manifolds and shown that the associated Nijenhuis tensor is conformally invariant under this transformation. We have also discussed the properties of contravariant almost analytic vector field, covariant almost analytic vector field and some other properties in almost Hermitian Manifold under this transformation.
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Study of a new type of metric connection in an almost Hermitian Manifold
2015Co-Authors: B B Chaturvedi, Pankaj PandeyAbstract:This paper contains the study of an almost Hermitian Manifold equippedwith a new type of metric connection.we have found the condition for an almostHermitian Manifold equipped with a new type of metric connection to be an almostK¨ahler Manifold. We have also studied contravariant almost analytic vector fieldin an almost Hermitian Manifold equipped with a new type of metric connection.Also, we have shown that the Lie derivative of the metric tensor is hybrid in analmost Hermitian Manifold equipped with a new type of metric connection.
Miguel Brozos-vázquez - One of the best experts on this subject based on the ideXlab platform.
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Geometric Realizations of Para-Hermitian Curvature Models
Results in Mathematics, 2009Co-Authors: Miguel Brozos-vázquez, Stana Nikcevic, Peter B. Gilkey, Ramón Vázquez-lorenzoAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri–Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
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Geometric Realizations of Hermitian curvature models
arXiv: Differential Geometry, 2008Co-Authors: Miguel Brozos-vázquez, Peter B. Gilkey, H. Kang, Stana NikcevicAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
Stana Nikcevic - One of the best experts on this subject based on the ideXlab platform.
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Geometric Realizations of Para-Hermitian Curvature Models
Results in Mathematics, 2009Co-Authors: Miguel Brozos-vázquez, Stana Nikcevic, Peter B. Gilkey, Ramón Vázquez-lorenzoAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri–Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
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Geometric Realizations of Hermitian curvature models
arXiv: Differential Geometry, 2008Co-Authors: Miguel Brozos-vázquez, Peter B. Gilkey, H. Kang, Stana NikcevicAbstract:We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian Manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.
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the local index formula for a Hermitian Manifold
Pacific Journal of Mathematics, 1997Co-Authors: Peter B. Gilkey, Stana Nikcevic, J PohjanpeltoAbstract:Let M be a compact complex Manifold of real dimension m = 2m with a Hermitian metric. Let an(x,∆) be the heat equation asymptotics of the complex Laplacian ∆. Then TrL2(fe−t∆ p,q ) ∼ Σn=0t ∫ M fan(x,∆) for any f ∈ C∞(M); the an vanish for n odd. Let ag(M) be the arithmetic genus and let an(x, ∂) := Σq(−1)an(x,∆) be the supertrace of the heat equation asymptotics. Then ∫ M an(x, ∂)dx = 0 if n 6= m while ∫ M am(x, ∂)dx = ag(M). The Todd polynomial Tdm is the integrand of the Riemann Roch Hirzebruch formula. If the metric on M is Kaehler, then the local index theorem holds:
