# Volume 26 (2018), Issue 2

### 1. A Study on ϕ-recurrence τ-curvature tensor in (k, µ)-contact metric manifolds

In this paper we study ϕ-recurrence τ -curvature tensor in (k, µ)-contact metric manifolds.

### 2. On some extremal problems in Bergman spaces in weakly pseudoconvex domains

We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂ n based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces A α p $A_\alpha ^p$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

### 3. Approach of q-Derivative Operators to Terminating q-Series Formulae

The q-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.

### 4. Geometry of Mus-Sasaki metric

In this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M as a new natural metric non-rigid on T M. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

### 5. A new class of almost complex structures on tangent bundle of a Riemannian manifold

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

### 6. A sequence adapted from the movement of the center of mass of two planets in solar system

In this paper we derive a sequence from a movement of center of mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.

### 7. New stability results for spheres and Wulff shapes

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp -sense is W 2 ,p -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].