A Class of Second Order Tangent Sets

Let [Formula: see text] be a pseudo-Riemannian manifold and [Formula: see text] be its second-order tangent bundle equipped with the deformed [Formula: see text]nd lift metric [Formula: see text] which is obtained from the [Formula: see text]nd lift metric by deforming the horizontal part with a symmetric [Formula: see text]-tensor field [Formula: see text]. In the present paper, we first compute the Levi-Civita connection and its Riemannian curvature tensor field of [Formula: see text]. We give necessary and sufficient conditions for [Formula: see text] to be semi-symmetric. Secondly, we show that [Formula: see text] is a plural-holomorphic [Formula: see text]-manifold with the natural integrable nilpotent structure. Finally, we get the conditions under which [Formula: see text] with the [Formula: see text]nd lift of an almost complex structure is an anti-Kähler manifold.

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Second order tangent bundles of infinite dimensional manifolds

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2004.02.005 ◽

2004 ◽

Vol 52 (2) ◽

pp. 127-136 ◽

Cited By ~ 8

Author(s):

C.T.J. Dodson ◽

G.N. Galanis

Keyword(s):

Second Order ◽

Infinite Dimensional ◽

Tangent Bundles ◽

Order Tangent

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New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization

Journal of Optimization Theory and Applications ◽

10.1007/s10957-016-1011-1 ◽

2016 ◽

Vol 172 (1) ◽

pp. 128-140 ◽

Cited By ~ 5

Author(s):

Zhenhua Peng ◽

Yihong Xu

Keyword(s):

Second Order ◽

Order Tangent

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Flattening properties of diffeomorphisms of the second-order tangent bundles induced by holomorphically projective diffeomorphisms of Kählerian spaces

Journal of Mathematical Sciences ◽

10.1007/s10958-012-1083-x ◽

2012 ◽

Vol 187 (5) ◽

pp. 550-573

Author(s):

K. M. Zubrilin

Keyword(s):

Second Order ◽

Tangent Bundles ◽

Order Tangent

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Generalized Geometry for Second Order Tangent Groups & Affine Configuration Complexes

10.20944/preprints202102.0223.v1 ◽

2021 ◽

Author(s):

Azhar Iqbal ◽

Gohar Ali ◽

Javed Khan

Keyword(s):

Second Order ◽

Generalized Geometry ◽

Higher Weights ◽

Order Tangent

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

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