Three dimensional 2-Hopf hypersurfaces with harmonic curvature

2021 ◽  
Vol 499 (1) ◽  
pp. 125005
Author(s):  
Yaning Wang
Keyword(s):  
Three Dimensional ◽  
Harmonic Curvature ◽  
Hopf Hypersurfaces

scholarly journals On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 559
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Weyl Curvature ◽  
Space Forms ◽  
Hopf Hypersurfaces ◽  
Weyl Curvature Tensor ◽  
New Type ◽  
Complex Space Forms

In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations.

scholarly journals A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 977-985 ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Recent Result ◽  
Three Dimensional ◽  
Local Symmetry ◽  
Kenmotsu Manifold ◽  
Harmonic Curvature ◽  
Riemannian Product ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Curvature Tensors

AbstractLet M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016, 45, 435-442].

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

Ultrastructural Investigations of the Contractile Filaments of Amoebae

1974 ◽  
Vol 32 ◽  
pp. 188-189
Author(s):  
P.L. Moore
Keyword(s):  
Cytoplasmic Streaming ◽  
Three Dimensional ◽  
Freeze Fracture ◽  
Amoeboid Movement ◽  
Different Types ◽  
Chemical Conditions ◽  
Complete Interpretation

Previous freeze fracture results on the intact giant, amoeba Chaos carolinensis indicated the presence of a fibrillar arrangement of filaments within the cytoplasm. A complete interpretation of the three dimensional ultrastructure of these structures, and their possible role in amoeboid movement was not possible, since comparable results could not be obtained with conventional fixation of intact amoebae. Progress in interpreting the freeze fracture images of amoebae required a more thorough understanding of the different types of filaments present in amoebae, and of the ways in which they could be organized while remaining functional.The recent development of a calcium sensitive, demembranated, amoeboid model of Chaos carolinensis has made it possible to achieve a better understanding of such functional arrangements of amoeboid filaments. In these models the motility of demembranated cytoplasm can be controlled in vitro, and the chemical conditions necessary for contractility, and cytoplasmic streaming can be investigated. It is clear from these studies that “fibrils” exist in amoeboid models, and that they are capable of contracting along their length under conditions similar to those which cause contraction in vertebrate muscles.

Structural organization of escherichia coli ribosomes as determined by immuno electron microscopy

1978 ◽  
Vol 36 (2) ◽  
pp. 166-167 ◽  
Author(s):  
G. Stöffler ◽  
R.W. Bald ◽  
J. Dieckhoff ◽  
H. Eckhard ◽  
R. Lührmann ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Escherichia Coli ◽  
Ribosomal Proteins ◽  
Structural Organization ◽  
Three Dimensional ◽  
Ribosomal Subunit ◽  
Spatial Arrangement ◽  
Small Subunit ◽  
Antibody Binding ◽  
Immuno Electron Microscopy

A central step towards an understanding of the structure and function of the Escherichia coli ribosome, a large multicomponent assembly, is the elucidation of the spatial arrangement of its 54 proteins and its three rRNA molecules. The structural organization of ribosomal components has been investigated by a number of experimental approaches. Specific antibodies directed against each of the 54 ribosomal proteins of Escherichia coli have been performed to examine antibody-subunit complexes by electron microscopy. The position of the bound antibody, specific for a particular protein, can be determined; it indicates the location of the corresponding protein on the ribosomal surface.The three-dimensional distribution of each of the 21 small subunit proteins on the ribosomal surface has been determined by immuno electron microscopy: the 21 proteins have been found exposed with altogether 43 antibody binding sites. Each one of 12 proteins showed antibody binding at remote positions on the subunit surface, indicating highly extended conformations of the proteins concerned within the 30S ribosomal subunit; the remaining proteins are, however, not necessarily globular in shape (Fig. 1).

Ribosome Structural Organization

1974 ◽  
Vol 32 ◽  
pp. 332-333
Author(s):  
James A. Lake
Keyword(s):  
Ribosomal Proteins ◽  
Structural Organization ◽  
Three Dimensional ◽  
Small Subunit ◽  
Structural Studies ◽  
X Ray Diffraction ◽  
Specific Antibodies ◽  
X Ray ◽  
E Coli ◽  
Complete Sequences

The understanding of ribosome structure has advanced considerably in the last several years. Biochemists have characterized the constituent proteins and rRNA's of ribosomes. Complete sequences have been determined for some ribosomal proteins and specific antibodies have been prepared against all E. coli small subunit proteins. In addition, a number of naturally occuring systems of three dimensional ribosome crystals which are suitable for structural studies have been observed in eukaryotes. Although the crystals are, in general, too small for X-ray diffraction, their size is ideal for electron microscopy.

Three-Dimensional Visualization of the T-System of Frog Muscle Using High Voltage Electron Microscopy and a Lanthanum Stain

1977 ◽  
Vol 35 ◽  
pp. 570-571 ◽  
Author(s):  
Lee D. Peachey ◽  
Clara Franzini-Armstrong
Keyword(s):  
Electron Microscopy ◽  
High Voltage ◽  
Three Dimensional ◽  
Biological Tissues ◽  
High Voltage Electron Microscopy ◽  
Transverse Tubular System ◽  
Peroxidase Reaction ◽  
Voltage Electron ◽  
High Voltage Electron ◽  
T System

The effective study of biological tissues in thick slices of embedded material by high voltage electron microscopy (HVEM) requires highly selective staining of those structures to be visualized so that they are not hidden or obscured by other structures in the image. A tilt pair of micrographs with subsequent stereoscopic viewing can be an important aid in three-dimensional visualization of these images, once an appropriate stain has been found. The peroxidase reaction has been used for this purpose in visualizing the T-system (transverse tubular system) of frog skeletal muscle by HVEM (1). We have found infiltration with lanthanum hydroxide to be particularly useful for three-dimensional visualization of certain aspects of the structure of the T- system in skeletal muscles of the frog. Specifically, lanthanum more completely fills the lumen of the tubules and is denser than the peroxidase reaction product.

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