Title
On Ruled Surfaces in threedimensional Minkowski Space,Used
Sold by Ergodebooks, an authorized reseller.
Returns accepted within 30 days | support@ergodebooks.com
Shipping Information
- Free Standard Shipping — United States only
- Processing Time: 1–3 business days
- Estimated Delivery: 3–5 business days after dispatch
- Double-boxed, fully insured & discreetly packaged
- Tracking number sent via email once dispatched
- Orders over $250 require signature upon delivery. Taxes calculated at checkout.
Returns & Refund
Returns accepted within 30 days of delivery.
Damaged or Defective Item
Free return shipping + replacement or full refund
Wrong Item Received
Free return shipping + replacement or full refund
Change of Mind
Return shipping at customer's expense · 25% restocking fee applies
Payment Option
In a Minkowski three dimensional space we define a semiinnerproduct based on the socalled cosineMinkowski function. We also construct an orthogonal 3D frame in Birkhoff sense, which is canonically adapted to ruled surfaces: beginning with the generator direction we complete this frame using the strictly convex and centrally symmetric unit ball B, which is described either by supporting function or vector representation. Based on the leftorthogonality defined by ball B, the striction curve of a ruled surface in a Minkowski 3space can be declared in analogy to the Euclidean case. We define the new vector called Deformation vector which helps us to find the FrenetSerret formulae of the ruled surface in the Minkowski three dimension spaces. In these formulae we insert the Mcurvatures and MTorsions with respect to the Minkowski frame. We also can define a covariant differentiation in a Minkowski 3space, with this can declare geometric Mparallelity of the vector field of the generator of a skew ruled surface along its Minkowski striction curve. Using the second fundamental form the relation between Euclidean and Minkowski normal vectors is given.
⚠️ WARNING (California Proposition 65):
This product may contain chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm.
For more information, please visit www.P65Warnings.ca.gov.