This paper aims to study the Berger type deformed Sasaki metric g_(BS)on the second order tangent bundle T^(2)M over a bi-Kählerian manifold M.The authors firstly find the Levi-Civita connection of the Berger typ...This paper aims to study the Berger type deformed Sasaki metric g_(BS)on the second order tangent bundle T^(2)M over a bi-Kählerian manifold M.The authors firstly find the Levi-Civita connection of the Berger type deformed Sasaki metric g_(BS)and calculate all forms of Riemannian curvature tensors of this metric.Also,they study geodesics on the second order tangent bundle T^(2)M and bi-unit second order tangent bundle T^(2)_(1,1)M,and characterize a geodesic of the bi-unit second order tangent bundle in terms of geodesic curvatures of its projection to the base.Finally,they present some conditions for a sectionσ:M→T^(2)M to be harmonic and study the harmonicity of the different canonical projections and inclusions of(T^(2)M,g_(BS)).Moreover,they search the harmonicity of the Berger type deformed Sasaki metric g_(BS)and the Sasaki metric g_(S) with respect to each other.展开更多
A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of...A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.展开更多
文摘This paper aims to study the Berger type deformed Sasaki metric g_(BS)on the second order tangent bundle T^(2)M over a bi-Kählerian manifold M.The authors firstly find the Levi-Civita connection of the Berger type deformed Sasaki metric g_(BS)and calculate all forms of Riemannian curvature tensors of this metric.Also,they study geodesics on the second order tangent bundle T^(2)M and bi-unit second order tangent bundle T^(2)_(1,1)M,and characterize a geodesic of the bi-unit second order tangent bundle in terms of geodesic curvatures of its projection to the base.Finally,they present some conditions for a sectionσ:M→T^(2)M to be harmonic and study the harmonicity of the different canonical projections and inclusions of(T^(2)M,g_(BS)).Moreover,they search the harmonicity of the Berger type deformed Sasaki metric g_(BS)and the Sasaki metric g_(S) with respect to each other.
文摘A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.
