Special Einstein's equations on K\"ahler manifolds

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov's classification of Riemannian manifolds according to special properties of the energy-momentum tensor to K\"ahler manifolds. We show that in this case the number of classes reduces.Comment: 5 page

The Radiocarbon Chronology of the Shan-Koba Rock-Shelter, a Late Paaleolithic an Mesoithic Sequence in the Crimean Mountains (Ukraine)

This paper presents a new series of AMS dates from the rock-shelter of Shan-Koba in the Crimean mountains (Ukraine). Four bone samples were selected at the Institute of Archaeology of the Academy of Sciences in St. Petersburg (Russian Federation), and AMS-dated at Groningen Isotopic Laboratory (Holland). The results show that the shelter was not “continuously” settled, as suggested by the excavators. In contrast they indicate that it was inhabited in well-defined periods between the end of the Palaeolithic (Allerød interstadial) and the end of the Mesolithic (Atlantic). Together with other radiocarbon dates recently obtained from the same sequence, as well as from Laspi 7 and Mirne, they help refine the absolute chronology of the Late Pleistocene and Early Holocene peopling of the north-western Black Sea region, and contribute to the study of the environmental and cultural changes that took place in the same territory at the boundary between the end of the Palaeolithic and the Atlantic climatic periods

The radiocarbon chronology of Shan-Koba rock-shelter, a Late Palaeolithic and Mesolithic sequence in the Crimean mountains (Ukraine)

Ovaj rad predstavlja novu seriju AMS datuma iz pripećka Šan-Koba u krimskim planinama (Ukrajina). Na Arheološkom institutu akademije znanosti u Sankt Peterburgu (Ruska Federacija) izabrana su četiri uzorka kosti koja su datirana AMS-om u izotopskom laboratoriju u Gröningenu (Nizozemska). Rezultati pokazuju da pripećak nije bio „neprekidno“ naseljen, na što su ukazivali istraživači. Suprotno tome, pokazuju da je bio nastanjen u precizno utvrđenim razdobljima od kraja paleolitika (interstadijal Allerød) do kraja mezolitika (atlansko klimatsko razdoblje). Zajedno s ostalim radiokarbonskim datumima nedavno dobivenim iz istog stratigrafskog slijeda, kao i iz Laspi 7 i Mirne, pomažu bolje utvrditi apsolutnu kronologiju obitavanja ljudi u sjeverozapadnoj regiji Crnog mora u kasnom pleistocenu i ranom holocenu te doprinijeti proučavanju okolišnih i kulturnih promjena koje su se dogodile na tom području na prijelazu između kraja paleolitika i atlantskog klimatskog razdoblja.This paper presents a new series of AMS dates from the rock-shelter of Shan-Koba in the Crimean mountains (Ukraine). Four bone samples were selected at the Institute of Archaeology of the Academy of Sciences in St. Petersburg (Russian Federation), and AMS-dated at Groningen Isotopic Laboratory (Holland). The results show that the shelter was not “continuously” settled, as suggested by the excavators. In contrast they indicate that it was inhabited in well-defined periods between the end of the Palaeolithic (Allerød interstadial) and the end of the Mesolithic (Atlantic). Together with other radiocarbon dates recently obtained from the same sequence, as well as from Laspi 7 and Mirne, they help refine the absolute chronology of the Late Pleistocene and Early Holocene peopling of the north-western Black Sea region, and contribute to the study of the environmental and cultural changes that took place in the same territory at the boundary between the end of the Palaeolithic and the Atlantic climatic periods

Einstein metrics in projective geometry

It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degerate normal solutions are equivalent to pseudo-Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.Comment: 10 pages. Adapted to published version. In addition corrected a minor sign erro

Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications

We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric $(0,2)-$tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed $(O(p+1,q),S^{p,q})$-manifold does not preserve any nondegenerate splitting of $\R^{p+1,q}$.Comment: minor correction

Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two

We prove an important partial case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the round sphere (up to a finite cover).Comment: 32 pages, one .eps figure. The version v1 has a misprint in Theorem 1: I forgot to write the assumption that the degree of mobility is greater than two. The versions v3, v4 have only cosmetic changes wrt v