Kadri Arslan

CONTACT CR-WARPED PRODUCT SUBMANIFOLDS IN KENMOTSU SPACE FORMS

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically im- mersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

CURVES AND SURFACES OF AW(k) TYPE

Bu calismada, AW(k) ( k=1, 2 yada 3 ) tipindeki egri ve yuzeyler gozonune alindi. AW(k) sartini saglayan egri ve yuzeylere ornekler verildi

Certain inequalities for submanifolds in ( K ,μ)-contact space forms

In (Ch3), B.Y. Chen established sharp relationship be- tween the Ricci curvature and the squared mean curvature for a submanifold in a Riemanian space form with arbitrary codimen- sion. In (MMO), one dealt with similar problems for submanifolds in complex space forms. In this article, we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in (k;�)-contact space forms.

BIHARMONIC SUBMANIFOLDS IN 3-DIMENSIONAL (κ,µ)-MANIFOLDS

Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of 3-dimensional (κ,μ)-manifolds to be biharmonic.

MERIDIAN SURFACES IN 4 WITH POINTWISE 1-TYPE GAUSS MAP

In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.

TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle c1 centered at origin with an Euclidean planar curve c2 has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle c1 centered at origin with an Euclidean planar curve c2 to have pointwise 1-type Gauss map.

Spherical Product Surfaces in E4

Abstract In the present study we calculate the coefficients of the second fundamental form and curvature ellipse of spherical product surfaces in E4. Otsuki rotational surfaces and Ganchev-Milousheva rotational surfaces are the special type of spherical product surfaces in E4. Further, we give necessary and sufficient condition for the origin of NpM to lie on the curvature ellipse of such surfaces. Finally we get the necessary condition for Ganchev-Milousheva rotational surfaces in E4 to become flat or Chen type. We also give some examples of the projections of these surfaces in E3

Ricci curvature of submanifolds in Kenmotsu space forms

In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al. In this paper, we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in Kenmotsu space forms.

A geometric description of the ascending colon of some domestic animals.

In this study, a geometric recognition of the ascending colons of some domestic animals such as pig, ruminants (only the ansa spiralis coli) and dog is presented. The ascending colon of these animals can be considered a tubular shape along a special curve.

A mathematical model of the ascending colon of the horse

In this study we present a geometric model of the ascending colon of the horse, especially the left ventral colon and the right ventral colon, the left dorsal colon and the right dorsal colon and the pelvic flexure. We also present a mathematical model of the cross sections of these ascending colon parts with the exceptions of the pelvic flexure. We show that these cross-sections correspond to the closed algebraic curves known as epitrochoid.