CRITICAL METRICS OF THE TRACE OF THE HEAT KERNEL ON A COMPACT MANIFOLD

Ahmad El Soufi (1) , Saïd Ilias (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

This paper is devoted to the study of critical metrics of the trace of the heat kernel on a compact manifold. We obtain various characterizations of such metrics and investigate their geometric properties. We also give a complete classification of critical metrics on surfaces of genus zero and one.

Mots clés: Laplacian; Heat kernel; Determinant of the Laplacian; Critical metrics

Domaines: Géométrie métrique [math.MG]

Ahmad El Soufi, Saïd Ilias. CRITICAL METRICS OF THE TRACE OF THE HEAT KERNEL ON A COMPACT MANIFOLD. Journal de Mathématiques Pures et Appliquées, 2002, 81, pp.1053-1070. ⟨hal-00002873⟩