In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M, any constant mean curvature H0 surface on one side of a constant mean curvature H0 surface Σ0 is an equidistant surface to Σ0. The main hypotheses of the theorem are that Σ0 is parabolic and the mean curvature of the equidistant surfaces to Σ0...

In this paper, we study the curvature of a semi-Riemannian manifold M̃ of quasi-constant curvature admits some half lightlike submanifolds M . The main result is two characterization theorems for M̃ admits extended screen homothetic and statical half lightlike submanifolds M such that the curvature vector field of M̃ is tangent to M .

Curvature collineations of a spray manifold induced by the Lie symmetries of the underlying spray are studied. The basic observation is that the Jacobi endomorphism and the Berwald curvature are invariant under these symmetries; this implies the invariance of the further curvature data. Our main technical tool is an appropriate Lie derivative operator along the tangent bundle projection. M.S.C....

Congenital fistulae between the tracheobronchial tree and oesophagus usually originate from the lower end of the trachea or right main bronchus. The case history is presented of a man in whom a fistula between the oesophagus and left main bronchus was not diagnosed until the age of 48.

Landslide is one of the natural disasters that occur in Malaysia. Topographic factors such as elevation, slope angle, slope aspect, general curvature, plan curvature, and profile curvature are considered as the main causes of landslides. In order to determine the dominant topographic factors in landslide mapping analysis, a study was conducted and presented in this paper. There are three main s...

introduction: complete knowledge of root canal curvature is a critical factor in successful dental treatment .the aim of this study was to investigate the direction, radius and degree of curvature of maxillary anterior teeth and the relation between radius and degree of curvature in babol city. methods &materials;: this study was performed on 242 anterior teeth radiographs were taken by periapi...

For a fixed n ∈ N, the curvature tensor of a pseudo-Riemannian metric, as well as its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less or equal than n. In this paper, we re-elaborate recent results by Gilkey-Park-Sekigawa regarding these p-covariant curvature identities, for p = 0, 2. To this end, we use the classical theory of natural operations, th...

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...

In this paper, we obtain the isoperimetric inequality on a conformally flat manifold with finite total Q-curvature. This is a higher dimensional analog of Li and Tam’s result [“Complete surfaces with finite total curvature.” Journal of Differential Geometry 33 (1991): 139–68] on surfaces with finite total Gaussian curvature. The main step in the proof is based on the construction of a quasiconf...