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A curvature identity on a 6-dimensional Riemannian manifold and its applications

Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa (2017)

Czechoslovak Mathematical Journal

We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a...

A description of derivations of the algebra of symmetric tensors

A. Heydari, N. Boroojerdian, E. Peyghan (2006)

Archivum Mathematicum

In this paper the symmetric differential and symmetric Lie derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frölicher-Nijenhuis bracket for vector valued symmetric tensors.

A differential geometric characterization of invariant domains of holomorphy

Gregor Fels (1995)

Annales de l'institut Fourier

Let G = K ℂ be a complex reductive group. We give a description both of domains Ω ⊂ G and plurisubharmonic functions, which are invariant by the compact group, K , acting on G by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space M : = G / K . Such an invariant domain Ω with a smooth boundary is Stein if and only if the corresponding domain Ω M ⊂ M is geodesically convex and the sectional curvature of its boundary S : = ∂ Ω M fulfills the condition K S ( E ) ≥ K M ( E ) + k ( E , n ) . The term k ( E , n ) is explicitly computable...

A discrete version of the Brunn-Minkowski inequality and its stability

Michel Bonnefont (2009)

Annales mathématiques Blaise Pascal

In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for metric measure spaces. Our new definition, based only on properties of the distance, allows also us to deal with discrete metric measure spaces. Then we show the stability of our new inequality under convergence of metric measure spaces. This result gives as corollary the stability of the classical Brunn-Minkowski inequality for geodesic spaces. The proof of this stability...

A few remarks on the geometry of the space of leaf closures of a Riemannian foliation

Małgorzata Józefowicz, R. Wolak (2007)

Banach Center Publications

The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in ℝ k for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space. In Section...

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