Conjugate connections with respect to a quadratic endomorphism and duality

Bejan, Cornelia-Livia; Crâşmăreanu, Mircea

doi:10.2298/fil1609367b

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…It is easy to see that ∇ * and ∇ † are indeed connections such that (∇ * ) * = ∇ † † = ∇. Another type of conjugate connections are those concerning with tensor structures (for details, [1,2,4]). In our setting, this connection is defined by…”

Section: Definition 2 [3]mentioning

confidence: 99%

Conjugate Connections and their Applications on Pure Metallic Metric Geometries

Durmaz¹,

Gezer²

2022

Preprint

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Let (M, J, g) be a metallic pseudo-Riemannian manifold equipped with a metallic structure J and a pseudo-Riemannian metric g. The paper deals with interactions of Codazzi couplings formed by conjugate connections and tensor structures. The presence of Tachibana operator and Codazzi couplings presented a new characterization for locally metallic pseudo-Riemannian manifold. Also, a necessary and sufficient condition a non-integrable metallic pseudo-Riemannian manifold is a quasi metallic pseudo Riemannian manifold is derived. Finally, it is introduced metallic-like pseudo-Riemannian manifolds and presented some results concerning them.

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Section: Definition 2 [3]mentioning

confidence: 99%

Conjugate Connections and their Applications on Pure Metallic Metric Geometries

Durmaz¹,

Gezer²

2022

Preprint

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“…The present paper deals with the study of these connections and then it is the fifth in a series containing [4], [5], [3] and [6]. We remark that Bejan and Crasmareanu [1] studied the conjugate connections with respect to a quadratic endomorphism as a generalization of almost complex and almost product cases. An important tool in our work is provided by the pair (structural tensor, virtual tensor) defined for the almost product geometry in [5] and considered here in the last part of Section 1.…”

Section: Introductionmentioning

confidence: 97%

“…Besides the very well known almost complex, almost tangent, and almost product structures on a differentiable manifold M , some other polynomial structures naturally arise as C ∞ -tensor fields J of type (1,1) which are roots of the algebraic equation Q(J) := J n + a n J n−1 + · · · + a 2 J + a 1 I X(M ) = 0, where I X(M ) is the identity map on the Lie algebra of vector fields on M . In particular, if the structure polynomial is Q(J) := J 2 − pJ − qI X(M ) , with p and q positive integers, its solution J will be called metallic structure [11].…”

Section: Introductionmentioning

confidence: 99%

Metallic conjugate connections

Blaga¹,

Hreƫcanu²

2017

Rev. Un. Mat. Argentina

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Properties of metallic conjugate connections are stated by pointing out their relation to product conjugate connections. We define the analogous in metallic geometry of the structural and the virtual tensors from the almost product geometry and express the metallic conjugate connections in terms of these tensors. From an applied point of view we consider invariant distributions with respect to the metallic structure and for a natural pair of complementary distributions, the above structural and virtual tensors are expressed in terms of O'Neill–Gray tensor fields.

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“…For more details on conjugate connections and their application to information theory, statistics and other fields see [2], [3], [7], [14], [17], [20]. Another kind of conjugate connections are those which are dual with respect to an invertible (1,1)-tensor field [1], [4]. Conjugate connections relative to an almost complex structure are studied by A. M. Blaga and M. Crasmareanu in [6].…”

Section: Introductionmentioning

confidence: 99%