Zobrazeno 1 - 10
of 136
pro vyhledávání: '"Koike, Naoyuki"'
Autor:
Koike, Naoyuki
In this paper, we introduce the notion of a regularizable submanifold in a Riemannian Hilbert manifold. This submanifold is defined as a curvature-invariant submanifold such that its shape operators and its normal Jacobi operators are regularizable,
Externí odkaz:
http://arxiv.org/abs/2311.10074
Autor:
Koike, Naoyuki
In this paper, we prove that there exists a $C^{\infty}$-Calabi-Yau structure on the whole of the complexification $G^{\mathbb C}/K^{\mathbb C}$ of a rank two symmetric space $G/K$ of compact type. The proof is performed by deriving a relation (which
Externí odkaz:
http://arxiv.org/abs/2309.17418
Autor:
Fujii, Tomoki, Koike, Naoyuki
In this paper, we consider translators (for the mean curvature flow) given by a graph of a function on a symmetric space $G/K$ of compact type which is invariant under a hyperpolar action on $G/K$. First, in the case of $G/K=SO(n+1)/SO(n)$, $SU(n+1)/
Externí odkaz:
http://arxiv.org/abs/2308.15790
Autor:
Koike, Naoyuki
Let $\pi:P\to B$ be a smooth $G$-bundle over a compact Riemannian manifold $B$ and $c$ a smooth loop in $B$ of constant seed $a(>0)$, where $G$ is compact semi-simple Lie group. In this paper, we prove that the holonomy map ${\rm hol}_c:\mathcal A_P^
Externí odkaz:
http://arxiv.org/abs/2206.12566
Autor:
Koike, Naoyuki
From the Lytchak's result for polar foliations on an irreducible simply connected symmetric space $G/K$ of compact type and rank greater than one, we can derive that there exists no equifocal submanifold with non-flat section whose codimension is gre
Externí odkaz:
http://arxiv.org/abs/2101.04331
Autor:
Koike, Naoyuki
In this paper, we investigate the preservability of the curvature-adaptedness along the mean curvature flow starting from a compact curvature-adapted hypersurface in locally symmetric spaces, where the curvature-adaptedness means that the shape opera
Externí odkaz:
http://arxiv.org/abs/2012.05864
Autor:
Koike, Naoyuki
In this paper, we show that $G$-invariant Calabi-Yau structures on the complexification $G^{\mathbb C}/K^{\mathbb C}$ of a symmetric space $G/K$ of compact type are constructed from solutions of a Monge-Amp$\grave{\rm e}$re type equation. Also, we gi
Externí odkaz:
http://arxiv.org/abs/2003.04118
Autor:
Koike, Naoyuki
Publikováno v:
Illinois Journal of Mathematics vol. 63 (2019) 575-600
It is known that there exist Calabi-Yau structures on the complexifications of symmetric spaces of compact type. In this paper, we describe the Calabi-Yau structures of the complexified symmetric spaces in terms of the Schwarz's theorem in detail. We
Externí odkaz:
http://arxiv.org/abs/1901.01667
Autor:
Koike, Naoyuki
In this paper, we investigate a regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric and almost free action of a Hilbert Lie group whose orbits are minimal regularizable submanifolds. W
Externí odkaz:
http://arxiv.org/abs/1811.03441
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