I'm learning to tongue. some say start without the tongue with just the abdominals. However when I do this, I cut the length of my note. I want to provide a smooth link with the next note, yet tongue all these notes. How best to do this?
I was taught to use the syllable "tooh" as it maintains ideal shape for your lips and oral cavity while keeping the tone focus. Using other syllables, such as "tuh" or "duh" spread the tone and change the shape of your lips and oral cavity.
Regarding airflow, stopping and starting notes only by stopping / starting airflow is what we refer to as "huffing", which is not ideal for creating musical phrasing, nor does it allow you the flexibility you need to articulate more complex passages. Sometimes music calls for a "breath accent", and if so, this technique should be employed (at least for starting that particular note).
Rather, you should visualize your air as a continuous stream (that complements musical phrasing) wherein your tongue momentarily interrupts the stream in order to articulate the necessary rhythms. "Huffing" tends to isolate notes within phrases, whereas air as a constant stream helps to create more coherent musical gestures.
Thinking of your air and tonguing in the way I've described will afford you the length, connectivity, and expressiveness that you're looking for.
If you're cutting the length of each note, you are probably starting a little late. Be gentle with the tonguing, it's not cork out of a bottle time. Either that, or you're cutting each note short in order to tongue the following note. Again, if you're more gentle, you don't have to take time getting that tongue right to the front of your mouth. Also, you don't need to take a breath in between each note, whether it's tongued or not. More of a duh than a tuh.
If you start a note with JUST air pressure, what you call "just the abdominals", it proves that your embouchure is set up correctly - you're not "kicking" the note into starting with violent tonguing. This may be why you've been recommended to practice this way. Or maybe you've fallen into the habit of starting AND ending a note with too much tongue, so your teacher feels removing tonguing altogether might cure this.
But, in real playing, we usually use SOME tongue to start a note (or a legato phrase). Maybe an almost imperceptible "duh", maybe a more percussive "tuh".
But take this up with your teacher. It's too easy to get the wrong message from a written opinion from someone who isn't hearing you play.