8 citations · 28 across the 19 of their papers we have counts for
11 papers · 1 filter
Rigidity of Lie foliations with locally symmetric leaves
Gael Meigniez, Hiraku Nozawa
We prove that if the leaves of a minimal Lie foliation are locally isometric to a symmetric space of non-compact type without a Poincare disk factor, then the foliation is smoothly…
Generalized Bishop frames on curves on E^4
Hiraku Nozawa, Subaru Nomoto
We introduce and study generalized Bishop frames on regular curves, which are generalizations of the Frenet and Bishop frames for regular curves on higher dimensional spaces. There…
Localization of Chern-Simons type invariants of Riemannian foliations
Oliver Goertsches, Hiraku Nozawa, Dirk Toeben
We prove an Atiyah-Bott-Berline-Vergne type localization formula for Killing foliations in the context of equivariant basic cohomology. As an application, we localize some Chern-Si…
Haefliger cohomology of complete Riemannian foliations
Hiraku Nozawa
Haefliger cohomology characterizes taut foliated manifolds by Haefliger's theorem. We show that Haefliger cohomology characterizes strongly tense foliated manifolds, namely, foliat…
Rigidity and vanishing of basic Dolbeault cohomology of Sasakian manifolds
Oliver Goertsches, Hiraku Nozawa, Dirk Toeben
The basic Dolbeault cohomology groups of a Sasakian manifold M are invariants of its characteristic foliation F (the orbit foliation of the Reeb flow). We show some fundamental pro…
Tenseness of Riemannian flows
Hiraku Nozawa, José Ignacio Royo Prieto
We show that any transversally complete Riemannian foliation F of dimension one on any possibly non-compact manifold M is tense; namely, (M,F) admits a Riemannian metric such that…
Continuity of the Alvarez class under deformations
Hiraku Nozawa
A foliated manifold (M,F) is minimizable if there exists a Riemannian metric g on M such that every leaf of F is a minimal submanifold of (M,g). Alvarez Lopez defined a cohomology…
Minimizability of developable Riemannian foliations
Hiraku Nozawa
Let (M,F) be a closed manifold with a Riemannian foliation. We show that the secondary characteristic classes of the Molino's commuting sheaf of (M,F) vanish if (M,F) is developabl…
Rigidity of the Alvarez class
Hiraku Nozawa
Let be a closed manifold with a Riemannian foliation. The Álvarez class is the cohomology class of degree 1 of whose triviality characterizes the minimizabili…
Rigidity of the Álvarez classes of Riemannian foliations with nilpotent structure Lie algebras
Hiraku Nozawa
We show that if the structure algebra of a Riemannian foliation F on a closed manifold M is nilpotent, then the integral of the Álvarez class of (M,F) along every closed path is th…
Deformation of Sasakian metrics
Hiraku Nozawa
Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-compon…