Given a constant vector field Z in Minkowski space, a timelike surface is said to have a canonical null direction with respect to Z if the projection of Z on the tangent space of the surface gives a lightlike vector field. For example in the three-dimensional Minkowski space: a surface has a canonical null direction if and only if it is minimal and flat. When the ambient has arbitrary dimension, if a surface has a canonical null direction and has parallel mean curvature vector then it is minimal. We give different ways for building these surfaces in the four-dimensional Minkowski space. On the other hand, we describe several properties in the non ruled general case in four-dimensional Minkowski space. One property is that the tangent part of Z is an asymptotic direction of the surface. We describe these surfaces in the ruled case in arbitrary dimension. Finally use the Gauss map for describe another properties of these surfaces in dimension four.
Journal of Geometry – Springer Journals
Published: May 30, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera