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21.
Shyuichi Izumiya 《Journal of Mathematical Sciences》2007,144(1):3789-3803
We construct a basic framework for studying the extrinsic differential geometry on time-like hypersurfaces in the de Sitter
space from the viewpoint of the theory of Legendrian singularities. As an application, we study the contact of time-like hypersurfaces
with flat totally umbilic time-like hypersurfaces in the de Sitter space.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal
Conference-2004, Part 1, 2005. 相似文献
22.
We study overdetermined systems of first order partial differential equations with singular solutions. The main result gives
a characterization of such systems and asserts that the singular solution is equal to the contact singular set. 相似文献
23.
We study timelike hypersurfaces in anti-de Sitter space from the viewpoint of the Lagrangian/ Legendrian singularity theory. 相似文献
24.
Shyuichi Izumiya Donghe Pei María del Carmen Romero Fuster 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):156-173
We define the notions of (S
t
1 × S
s
2)-nullcone Legendrian Gauss maps and S
+2-nullcone Lagrangian Gauss maps on spacelike surfaces in anti de Sitter 4-space. We investigate the relationships between
singularities of these maps and geometric properties of surfaces as an application of the theory of Legendrian/Lagrangian
singularities. By using S
+2-nullcone Lagrangian Gauss maps, we define the notion of S
+2-nullcone Gauss-Kronecker curvatures and show a Gauss-Bonnet type theorem as a global property. We also introduce the notion
of horospherical Gauss maps which have geometric properties different from those of the above Gauss maps. As a consequence,
we can say that anti de Sitter space has much richer geometric properties than the other space forms such as Euclidean space,
hyperbolic space, Lorentz-Minkowski space and de Sitter space. 相似文献
25.
26.
We consider extrinsic differential geometry on spacelike hypersurfaces in Minkowski pseudo-spheres (hyperbolic space, de Sitter space and the lightcone). In the previous paper [S. Izumiya, Legendrian dualities and spacelike hypersurfaces in the lightcone, Preprint] we have shown a basic Legendrian duality theorem between pseudo-spheres. We define the spacelike parallels by using the basic Legendrian duality theorem. This definition unifies the notions of parallels of spacelike hypersurfaces in pseudo-spheres. We also define the evolute as the locus of singularities of the spacelike parallels. These notions are investigated as applications of Lagrangian or Legendrian singularity theory. We consider geometric properties of non-singular spacelike hypersurfaces corresponding to singularities of spacelike parallels or evolutes. 相似文献
27.
Oguri H Maeda N Izumiya C Kusume T Yamamoto Y Fukaya T 《Magnetic resonance imaging》2004,22(9):1333-1337
The incidence of cervical adenocarcinoma is increasing. Nabothian cysts are a common gynecologic condition; if multiple and/or large cysts are present, it is difficult to differentiate them from a minimal-deviation adenocarcinoma (MDA), which is classified as a special type of cervical adenocarcinoma. We report three cases of deep nabothian cysts and three cases of MDAs. Magnetic resonance imaging (MRI) findings, signs, and symptoms of these cases are described. The absence of a watery discharge and an MR image displaying a round or oval cyst without enhancement after intravenous gadolinium are helpful in the diagnosis of a deep nabothian cyst. 相似文献
28.
29.
Izumiya S.; Pei D.; Fuster M. C. Romero; Takahashi M. 《Journal London Mathematical Society》2005,71(3):779-800
Some geometrical properties associated to the contact of submanifoldswith hyperhorospheres in hyperbolic n-space are studied as anapplication of the theory of Legendrian singularities. 相似文献
30.
Yasuyuki Shimohigashi Tetsuo Kato Shinwon Kang Yoshihiro Minematsu Michinori Waki Nobuo Izumiya 《Tetrahedron letters》1979,20(15):1327-1328
The chemical shift of amide protons of acylamine acids showed a linear relation with electronegativity of the acyl groups. Prediction of the carbonyl group participated in intramolecular hydrogen bonding was discussed, gramiciding S being used as an example. 相似文献