Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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The Foundations Of Differential Geometry

The Jacobi inversion theorem leads to functions of several variables with many periods. So, we are led to the problem of developing a theory of them which is analogous to the theory of elliptic functions. First of all, we need to give an introduction to the theory of functions of several complex variables. In this chapter, we give an elementary introduction which essentially follows Weierstrass. One of the main topics will be the proof of the theorem that any meromorphic function on ℂn can be written as a quotient of two entire functions. Weierstrass called this a very difficult problem. The first proof was given by Poincare. In the case n = 1, it is not difficult to show this by means of the theory of Weierstrass products, even for arbitrary domains D ⊂ ℂ instead of ℂ. The case n > 1 is more involved, since the zero sets and pole sets of analytic functions of several complex variables are not discrete.

Analytic Functions of Several Complex Variables

Book review: Applied cryptography: Protocols, algorithms, and source code in C

Manifolds all of whose geodesics are closed

We prove, in a purely geometric way, that there are no connected irreducible proper subgroups of SO(N,1). Moreover, a weakly irreducible subgroup of SO(N,1) must either act transitively irreducible subgroup of SO(N,1) must either act transitively on the hyperbolic space or on a horosphere. This has obvious consequences for Lorentzian holonomy and in particular explains clasification results of Marcel Berger's list (e.g. the fact that an irreducible Lorentzian locally symmetric space has constant curvatures). We also prove that a minimal homogeneous submanifold of hyperbolic space must be totally-geodesic.

The geometry of homogeneous submanifolds of hyperbolic space

A submanifold of $${\mathbb {R}^n}$$
 whose tangent space makes constant angle with a fixed direction d is called a helix. In the first part of the paper we study helix hypersurfaces. We give a local description of how these hypersurfaces are constructed. As an application we construct (nonflat) minimal helices hypersurfaces in $${\mathbb {R}^n}$$
 for n > 3. In the second part we give a characterization of helix submanifolds related to the solutions of the so called eikonal differential equation. As a corollary we give necessary and sufficient conditions for a manifold M to be immersed as an helix in some Euclidean space. In the third part of this paper we study r-helices submanifolds. That is to say submanifolds such that its tangent space makes a constant angle with r linearly independent directions.

Helix submanifolds of euclidean spaces

In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On the one hand we completely classify the h.K.m. which can be Kaehler immersed into a finite or infinite dimensional complex Euclidean or hyperbolic space. On the other hand, we extend known results about Kaehler immersions into the finite dimensional complex projective space to the infinite dimensional setting

https://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2012/0016/0003/AJM-2012-0016-0003-a007.pdf

Kähler immersions of homogeneous Kähler manifolds into complex space forms

Symplectic duality of symmetric spaces

A submanifold of Rn whose tangent space makes constant angle with a fixed direction d is called a helix. Helix submanifolds are related with the eikonal PDE equation. We give a method to find every solution to the eikonal PDE on a Riemannian manifold locally. As a consequence we give a local construction of arbitrary Euclidean helix submanifolds of any dimension and codimension. Also we characterize the ruled helix submanifolds and in particular we describe those which are minimal.

https://projecteuclid.org/download/pdf_1/euclid.kmj/1278076336

Antonio J. Di Scala

Papers

The geometry of homogeneous submanifolds of hyperbolic space

Helix submanifolds of euclidean spaces

Kähler immersions of homogeneous Kähler manifolds into complex space forms

Symplectic duality of symmetric spaces

Higher codimensional Euclidean helix submanifolds