Einstein warped product spaces on Lie groups

• Autores: Buddhadev Pal, Santosh Kumar, Pankaj Kumar
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 3, 2022, págs. 485-500
• Idioma: inglés
• DOI: 10.56754/0719-0646.2403.0485
• Enlaces
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• Resumen
  • español

    Resumen Consideramos un grupo de Lie compacto con métrica bi-invariante, que proviene de la forma de Killing. En este artículo estudiamos espacios productos alabeados de Einstein, M = M1 × f 1 M2 para los casos (i) M1 es un grupo de Lie (ii) M2 es un grupo de Lie y (iii) ambos M1 y M2 son grupos de Lie. Más aún, obtenemos condiciones para que un producto alabeado de Einstein de grupos de Lie sea una variedad producto simple. Luego, caracterizamos la función de alabeo para el espacio-tiempo generalizado de Robertson-Walker, (M = I ×f 1 G2, −dt 2 + f 1 2 g2 cuya fibra G2 es un grupo de Lie compacto semi-simple de dim G2 > 2 con una métrica bi-invariante, que proviene de la forma de Killing.

  • English

    Abstract We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, M = M1× f1 M2 for the cases, (i) M1 is a Lie group (ii) M2 is a Lie group and (iii) both M1 and M2 are Lie groups. Moreover, we obtain the conditions for an Einstein warped product of Lie groups to become a simple product manifold. Then, we characterize the warping function for generalized Robertson-Walker spacetime, (M = I ×f 1 G2, −dt 2 + f 1 2 g2 whose fiber G2, being semi-simple compact Lie group of dim G2 > 2, having bi-invariant metric, coming from the Killing form.

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