As it is well-known, the geometry of curve in three-dimensions is actually characterized by Frenet vectors. In this paper, we obtain Smarandache curves by using cone frame formulas in null cone Q3 . Also, we give an example related to these curves.

In this paper, we give Smarandache curves according to the asymptotic orthonormal frame in null cone Q2. By using cone frame formulas, we present some characterizations of Smarandache curves and calculate cone frenet invariants of these curves. Also, we illustrate these curves with an example.

As it is well-known, the geometry of curve in three-dimensions is actually characterized by Frenet vectors. In this paper, we obtain Smarandache curves by using cone frame formulas in null cone Q3 . Also, we give an example related to these curves.

The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!

In this paper, we study the Smarandache curves according to the asymptotic orthonormal frame in Null Cone Q3. By using cone frame formulas, we obtain some characterizations of the Smarandache curves and introduce cone frenet invariants of these curves.