Search results for "Frölich"
showing 4 items of 4 documents
The exterior derivative as a Killing vector field
1996
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.
Graded Poisson structures on the algebra of differential forms
1995
We study the graded Poisson structures defined on Ω(M), the graded algebra of differential forms on a smooth manifoldM, such that the exterior derivative is a Poisson derivation. We show that they are the odd Poisson structures previously studied by Koszul, that arise from Poisson structures onM. Analogously, we characterize all the graded symplectic forms on ΩM) for which the exterior derivative is a Hamiltomian graded vector field. Finally, we determine the topological obstructions to the possibility of obtaining all odd symplectic forms with this property as the image by the pullback of an automorphism of Ω(M) of a graded symplectic form of degree 1 with respect to which the exterior der…
Brief an Garlieb H. Merkel
1799
Ms. 930a, Nr. 8, Bl. 22r-23v Böttiger, Karl August. Brief an Garlieb H. Merkel, Weimar, d[en] 13. November 1797 Autora rokraksts / Autograph, vācu, angļu un latīņu val. / Deutsch, Englisch und Latein [4] lpp. / S. Attēlu numuri / Bildnummern: 930a-008-1 – 930a-008-4 Der Verfasser nennt in diesem inhaltsreichen Brief zahlreiche Namen und hält nicht nur die Verbindung mit Merkel, die aus dessen erstem Aufenthalt in Weimar resultierte, aufrecht, sondern gibt ihm weitere Hinweise und Empfehlung für seinen weiteren Aufenthalt in Dänemark. So rät er zur Übersetzung dreier Romane aus dem Englischen, darunter Jane Wests „A gossip's story“ (London 1796). Ferner bittet der Verfasser Merkel um Gefälli…
Poisson-Nijenhuis structures and the Vinogradov bracket
1994
We express the compatibility conditions that a Poisson bivector and a Nijenhuis tensor must fulfil in order to be a Poisson-Nijenhuis structure by means of a graded Lie bracket. This bracket is a generalization of Schouten and Frolicher-Nijenhuis graded Lie brackets defined on multivector fields and on vector valued differential forms respectively.