The Geometry of Walker Manifolds

Brozos‐Vázquez, Miguel; Garcı́a-Rı́o, Eduardo; Gilkey, Peter Β.; Nikčević, Stana; Vázquez-Lorenzo, Ramón

doi:10.2200/s00197ed1v01y200906mas005

Cited by 84 publications

(130 citation statements)

References 167 publications

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“…The above structures were taken from [14,28]. The following result shows that the class of isotropic Kähler structures is larger than might at first sight be expected: …”

Section: Where G Is the Equivalence Class Of G And F(e F G)mentioning

confidence: 96%

Conformal Weyl-Euler-Lagrangian equations on 4-Walker manifolds

Kasap¹

2016

ntmsci

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Abstract:The main purpose of the present paper is to study almost complex structures conformal Weyl-Euler-Lagrangian equations on 4-dimensional Walker manifolds for (conservative) dynamical systems. In this study, routes of objects moving in space will be modeled mathematically on 4-dimensional Walker manifolds that these are time-dependent partial differential equations. A Walker n-manifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r ≤ n 2 . It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. Then, here we present complex analogues of Lagrangian mechanical systems on 4-Walker manifold. Also, the geometrical-physical results related to complex mechanical systems are also discussed for conformal Weyl-EulerLagrangian equations for (conservative) dynamical systems and solution of the motion equations using Maple Algebra software will be made.

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“…The above structures were taken from [14,28]. The following result shows that the class of isotropic Kähler structures is larger than might at first sight be expected: …”

Section: Where G Is the Equivalence Class Of G And F(e F G)mentioning

confidence: 96%

Conformal Weyl-Euler-Lagrangian equations on 4-Walker manifolds

Kasap¹

2016

ntmsci

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“…Эти многообразия называют-ся многообразиями Волкера (см. [4]). На всяком таком многообразии (M, g) существуют локальные координаты v, x 1 , .…”

Section: § 1 введение и основные результатыunclassified

Конформно Плоские Лоренцевы Многообразия Со Специальными Группами Голономии

Galaev¹

2013

Математический сборник

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Конформно плоские лоренцевы многообразия со специальными группами голономииПолучена локальная классификация конформно плоских лоренцевых многообразий со специальными группами голономии. Соответствующие локальные метрики представляют собой некоторые расширения римано-вых метрик постоянной секционной кривизны до метрик Волкера.Библиография: 28 названий.Ключевые слова: лоренцево многообразие, специальная группа голо-номии, многообразие Волкера, конформно плоское многообразие, теория гравитации Нордстрёма.

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“…Among these, the significant Walker manifolds are examples of the non-symmetric and non-homogeneous Osserman manifolds [2,3]. Recently, it was shown [4,6,7] that the Walker 4-manifolds of neutral signature admit a pair comprising an almost complex structure and an opposite almost complex structure, and that Petean's nonflat indefinite Kahler-Einstein metric on a torus was obtained as an example of a Walker 4-manifold.…”

Section: Introductionmentioning

confidence: 99%