Related papers: Some Open Problems in Sasaki Geometry
The object of this paper is to study the invariant submanifolds of Sasakian generalized-Sasakian-space-form. Here, we obtain some equivalent conditions for an invariant submanifold of a Sasakian generalized-Sasakian-space-forms to be…
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.
We study (transverse) scalar curvature type equation on compact Sasaki manifolds, in view of recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of K\"ahler metrics with constant scalar curvature (csck) on compact K\"ahler…
Generalized (\kappa ,\mu)-space forms are introduced and studied. We examine in depth the contact metric case and present examples for all possible dimensions. We also analyse the trans-Sasakian case.
We generalize problems in Wasan geometry which involve no folded figures but are related to Haga's fold in origami. Using the tangent circles appeared in those problems we give a parametric representation of the generalized Haga's fold…
A list of open problems on holomorphic symplectic, contact and Poisson manifolds.
The aim of this paper is to study compact 5--manifolds which carry a positive Sasakian structure. Strong restrictions are derived for the integral homology groups. In some cases, all positive Sasakian structures are classified. A key step…
We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal…
We study the fundamental groups of compact Sasakian manifolds, which we call Sasaki groups. It is shown that all known K$\ddot{a}$hler groups are Sasaki, in particular, all finite groups are Sasaki. On the other hand, we show there exists…
We give a brief introduction to theories with extra dimensions. We first introduce the basic formalism for studying extra-dimensional theories, including the Kaluza-Klein decomposition and the effective theory for 3-branes. We then focus on…
We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact…
This is a pedagogical introduction into theories with branes and extra dimensions. We first discuss the construction of such models from an effective field theory point of view, and then discuss large extra dimensions and some of their…
We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we…
This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal,…
This is the expanded version of my talk at the workshop "Groups of Automorphisms in Birational and Affine Geometry", October 29--November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the…
This is my Ph.D. Thesis at Tohoku Univeristy (July 2018). It presents the theory on shape derivatives and focuses on its applications to two-phase optimization problems. In particular, we treat the two-phase torsion problem and a two-phase…
The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop on Convex and Abstract Polytopes at the Banff International…
In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic…
We investigate several topics of the geometry on real Cayley-Klein spaces. An important concern for us is to define a distance function on the projective space in such a way that the distance between two anisotropic subspaces of the same…
In this expository article we first give an overview on multiplier ideal sheaves and geometric problems in K\"ahlerian and Sasakian geometries. Then we review our recent results on the relationship between the support of the subschemes cut…