A Surface Family with a Common Asymptotic Null Curve in Minkowski 3-Space <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.0608pt" id="M1" height="20.3615pt" version="1.1" viewBox="-0.0657574 -15.3007 17.3744 20.3615" width="17.3744pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g197-16" d="M567 0V44H236V319H535V363H236V618H567V662H70V0H567ZM192 44H114V618H192V44Z"/></g><g transform="matrix(.012,0,0,-0.012,10.674,-7.578)"><path id="g50-52" d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"/></g><g transform="matrix(.012,0,0,-0.012,10.674,4.995)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g></svg>

<div>The graph of the surface <i>M</i>.</div>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: A Surface Family with a Common Asymptotic Null Curve in Minkowski 3-Space <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.0608pt" id="M1" height="20.3615pt" version="1.1" viewBox="-0.0657574 -15.3007 17.3744 20.3615" width="17.3744pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g197-16" d="M567 0V44H236V319H535V363H236V618H567V662H70V0H567ZM192 44H114V618H192V44Z"/></g><g transform="matrix(.012,0,0,-0.012,10.674,-7.578)"><path id="g50-52" d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"/></g><g transform="matrix(.012,0,0,-0.012,10.674,4.995)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g></svg> 