A note on generalized S-space-forms

关于模形式与广义反常消去公式2的注记

A note on modular forms and generalized anomaly cancellation formulas 2

本文推广了(a,b)型消去公式至偶数维黎曼流形，并通过超渡得到奇数维流形上具有模性的特征形式。

A note on quasi generalized CR-lightlike geometry in indefinite nearly $μ$-Sasakian manifold

The concept of quasi generalized CR-lightlike was first introduced by the authors in [18]. In this paper, we focus on ascreen and co-screen quasi generalized CR-lightlike submanifolds of indefinite nearly $μ$-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi generalized CR-lightlike submanifolds admitting a metric connection. Classification theorems on nearly parallel and auto-parallel distributions on a co-screen quasi generalized CR-lightlike submanifold are also given. Several examples are also constructed, where necessary, to illustrate the main ideas.

A note on some generalized curvature tensor

For any semi-Riemannian manifold (M,g) we define some generalized curvature tensor as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold. That tensor is closely related to quasi-Einstein spaces, Roter spaces and some Roter type spaces.

Some notes on $LP$-Sasakian Manifolds with Generalized Symmetric Metric Connection

The present study initially identify the generalized symmetric connections of type $(α,β)$, which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when $(α,β)=(1,0)$ and $(α,β)=(0,1)$. Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ri…

A note on generalized Dirac eigenvalues for split holonomy and torsion

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\inΛ^3 M$ in the situation where the tangent bundle splits under the holonomy of $\nabla$ and the torsion of $\nabla$ is of `split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

A short note on biharmonic submanifolds in non-Sasakian contact metric 3-manifolds

We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(κ, μ)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of biharmonic submanifolds in a certain $3$-dimensional generalized $(κ, μ)$-manifold. Moreover, we determine $3$-dimensional generalized $(κ, μ)$-manifolds which admit a certain kind of proper biharmonic foliation.

A note on generalized laplacians and minimal surfaces

In these notes we give an interdisciplinary result which links the geometric concept of minimal surfaces with generalized harmonic functions.

Lecture notes on generalized Monge-Ampère equations and subvarieties

These are the lecture notes for the Morningside Center of Mathematics Geometry Summer School on August 15-20, 2022. These lectures sketch the results by Yau, Demailly-Paun, the author, and Datar-Pingali about generalized Monge-Ampère equations and subvarieties and aim to use these results to study the Hodge conjecture.

关于广义数值准则

On the generalized numerical criterion

本文通过给出具体实例，证明了对的广义数值准则问题的答案是否定的。

A note on generalized Thurston--Bennequin inequalities

We give a generalized Thurston--Bennequin-type inequality for links in $S^3$ using a Bauer--Furuta-type invariant for 4-manifolds with contact boundary. As a special case, we also give an adjunction inequality for smoothly embedded orientable surfaces with negative intersection in a closed oriented smooth 4-manifold whose non-equivariant Bauer--Furuta invariant is non-zero.

关于带临界强制项的广义 BV 平均曲率流的注记

A note on generalized BV mean curvature flow with a critical forcing term

本文注记证明了Liu–Tonegawa的带临界强制项的弱平均曲率流是广义BV流，确定了Brakke流满足面积变化公式的最小条件，推导了相关流的灭绝时间下界并概述了紧性定理的证明。

A note on the generalized Weierstrass representation

The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we establish a connection with the Weingarten surfaces. We suggest also a possible generalization for two-dimensional surfaces immersed in a flat space R^8 with Euclidean metric.

Duistermaat-Heckman formula for a torus action on a generalized Calabi-Yau manifold and localization formula

This note is an addendum to our earlier work \cite{humi}. In \cite{humi}, we studied a Hamiltonian action for a generalized Calabi-Yau manifold and showed that the Duistermaat-Heckman theorem holds. The purpose of this note is to show that the density function of the Duistermaa-Heckman measure is a piecewise polynomial. We also prove that the localization formula holds.

A note on Concircular Structure space-times

In this note we show that Lorentzian Concircular Structure manifolds (LCS)_n coincide with Generalized Robertson-Walker space-times.