Submanifolds with Parallel Fundamental Form

2000 ◽  
pp. 779-864 ◽  
Author(s):  
Ülo Lumiste
Keyword(s):  
Fundamental Form

Memory and Human Nature and our Developments: Hypothesis from Narrow Dimensions and Generalized Dimensions

2010 ◽  
Vol 33 ◽  
pp. 469-473
Author(s):  
K. Yu ◽  
J.W. Luo
Keyword(s):  
Human Nature ◽  
Fundamental Form ◽  
Basic Functions ◽  
Ancient Times ◽  
Generalized Dimensions ◽  
And Function ◽  
Original Feature

Memory in the nature of primitive features and basic functions, which plays an important role in promoting all the developments from ancient times to nowadays, is the most fundamental form of human nature. This paper will, from both narrow dimensions and generalized dimensions hypothesize and analyze the connection between memory and human nature or our developments; the original feature and function of memory, thereby, will be revealed.

scholarly journals First eigenvalue of submanifolds in Euclidean space

2000 ◽  
Vol 24 (1) ◽  
pp. 43-48
Author(s):  
Kairen Cai
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
The Second Fundamental Form ◽  
Compact Submanifold

We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.

Erkenntnis und Liebe. Zur Nähe und Ferne zwischen Heinrich Barths und Søren Kierkegaards Verständnis von Gemeinschaft

2018 ◽  
Vol 23 (1) ◽  
pp. 291-309 ◽  
Author(s):  
Anna Berres
Keyword(s):  
Present Article ◽  
Fundamental Form ◽  
Human Existence ◽  
History Of ◽  
The Will

AbstractAppearances to the contrary notwithstanding, the present article belongs neither in the category of source-work studies nor in that of history of reception; for it aims, in a purely systematical fashion, to outline and at the same time facilitate and prepare for a dialogue between Karl Barth’s lesser-known brother, philosopher Heinrich Barth (1890 – 1965), and Kierkegaard: in particular, between their—as it turns out, strikingly similar or at least complementary—views on human existence as co-existence or as a fundamental form of (being in) community. Accordingly, the article does not rest content with, much less restrict itself to a mere comparison and/or paraphrase of the respective views. It much rather seeks to explore critically the key claims: (a) human existence is essentially co-existence or being in community; (b) co-existence is basically dialogical, hence language-dependent; (c) dialogues must be performed in order possibly to be successful; (d) their actual success is a matter of contingency and thus cannot be guaranteed by a mere fiat of the will.

scholarly journals Classification of Some Special Types Ruled Surfaces in Simply Isotropic 3-Space

2017 ◽  
Vol 55 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Murat Kemal Karacan ◽  
Dae Won Yoon ◽  
Nural Yuksel
Keyword(s):  
Real Number ◽  
Laplace Operator ◽  
Fundamental Form ◽  
Three Dimensional ◽  
Ruled Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
The Laplace Operator ◽  
First Fundamental Form

AbstractIn this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I13under the condition ∆xi= λixiwhere ∆ is the Laplace operator with respect to the first fundamental form and λ is a real number. We also give explicit forms of these surfaces.

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