An Invitation to Lorentzian Geometry

Müller, Olaf; Sánchez, Miguel Azpitarte

doi:10.1365/s13291-013-0076-0

Cited by 16 publications

(16 citation statements)

References 104 publications

(128 reference statements)

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“…Let us discuss briefly the three alternative properties in the previous theorem (a more detailed discussion with further references can be found in [15]). …”

Section: Framework Of Lorentzian Manifolds and Relativistic Spacetimesmentioning

confidence: 99%

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Myers and Hawking Theorems: Geometry for the Limits of the Universe

Morales-Álvarez

Sánchez

2015

Milan J. Math.

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It is known that the celebrated theorem by Hawking which assures the existence of a Big-Bang under physically motivated hypotheses, uses geometric ideas inspired in classical Myers theorem. Our aim here is to go a step further: first, a result which can be interpreted as the exact analogy in pure Riemannian geometry to Hawking theorem will be proven and, then, the isomorphic role of the hypotheses in both theorems will be analyzed. This will provide some interesting links between Riemannian and Lorentzian geometries, as well as an introduction to the latter.The reader interested only in Riemannian Geometry can regard this new result as a simple application of Myers theorem combined with the properties of focal points. However, readers with broader perspectives will learn that when a geometer thinks in our space as a complete Riemannian manifold, a relativist may think in our spacetime as predictable, or that suitable bounds on the Ricci tensor will force geodesics either to converge in the space or to join in the time. Moreover, the limitation of the distance from any point to a hypersurface in a Riemannian manifold, may turn out into a catastrophic relativistic limit for the duration of our physical Universe.Mathematics Subject Classification. Primary 53C50, 53C20; Secondary 53C21, 83C75.

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“…Let us discuss briefly the three alternative properties in the previous theorem (a more detailed discussion with further references can be found in [15]). …”

Section: Framework Of Lorentzian Manifolds and Relativistic Spacetimesmentioning

confidence: 99%

“…See http://www.nobelprize.org/nobel prizes/physics/laureates/2011 4 Among the latter, one has Penrose's cosmic censorship hypothesis, see for example[7,15].…”

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confidence: 99%

Myers and Hawking Theorems: Geometry for the Limits of the Universe

Morales-Álvarez

Sánchez

2015

Milan J. Math.

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“…В работах [16], [97], [101] изучаются различные глобальные геометрические свойства лоренцевых многообразий с разными группами голономии. Группы голономии обсуждаются в недавнем обзоре по глобальной лоренцевой геометрии [105]. В [16] рассматриваются лоренцевы многообразия с несвязными группами голономии, приводятся примеры.…”

Section: а с галаевunclassified

Holonomy groups of Lorentzian manifolds

Galaev¹

2015

Uspekhi Mat. Nauk

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В работе дан обзор недавних результатов о классификации связных групп голономии лоренцевых многообразий. Получено упрощение конструкции лоренцевых метрик со всеми возможными связными группами голономии. В качестве применений рассмотрены уравнение Эйнштейна, лоренцевы многообразия с параллельными и рекуррентными спинорными полями, конформно плоские метрики Волкера и классификация 2-симметрических лоренцевых многообразий. Библиография: 123 названия. Ключевые слова: лоренцево многообразие, группа голономии, алгебра голономии, многообразие Волкера, уравнение Эйнштейна, рекуррентное спинорное поле, конформно плоское многообразие, 2-симметрическое лоренцево многообразие.

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“…Lorentz uzayı sahip olduğu özellikler itibarıyla, sınıflandırmada kullanılmak üzere yüksek bir potansiyele sahiptir. Lorentz uzayı genellikle fizikte Genel ve Özel Görecelik Kuramında, matematikte ise uzaylar teorisi ve diferansiyel geometride incelenen bir konudur [2].…”

Section: Introductionunclassified

Classification with Lorentzian distance metric

Bilge

Kerimbekov²

2015

2015 23nd Signal Processing and Communications Applications Conference (SIU)

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Özetçe-Bu çalışmada sınıflandırmada kullanılabilecek yeni bir uzaklık ölçütü önerilmiş ve başarısı irdelenmiştir. Lorentz uzayının sahip olduğu özel uzaklık metriğinden yararlanarak sınıflandırma başarısı artırılmıştır. Verilerin Öklid uzayından Lorentz uzayına taşınmasında en iyi başarıyı verecek olan açının bulunması için Destek Vektör Makinası karar çizgisinden yararlanılmıştır. WINE, ECOLI, BLOGGER, DIABET açık kaynaklı veri kümeleri ile deneysel çalışmalar yapılıp yöntemin başarısı incelenmiştir. Anahtar Kelimeler-Lorentz uzayı; uzaklık ölçütü; sınıflandırma.Abstract-In this study, a new distance metric that can be used in classification is proposed and its success is investigated. The classification success is increased by using the special distance metric in Lorentzian space. In order to find the optimum angle in transformation from Euclidean space to Lorentzian space, the decision line from Support Vector Machine is utilized. In experimental studies, the success of the proposed method is investigated by using open source data sets; WINE, ECOLI, BLOGGER, DIABET.

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An Invitation to Lorentzian Geometry

Cited by 16 publications

References 104 publications

Myers and Hawking Theorems: Geometry for the Limits of the Universe

Myers and Hawking Theorems: Geometry for the Limits of the Universe

Holonomy groups of Lorentzian manifolds

Classification with Lorentzian distance metric

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